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<rss xmlns:atom="http://www.w3.org/2005/Atom" version="2.0" xmlns:dc="http://purl.org/dc/elements/1.1/"><channel><title>BioIFT tutorials</title><link>http://mathbio.github.io/</link><description>Interesting stuff on Mathematical Biology.</description><atom:link rel="self" href="http://mathbio.github.io/rss.xml" type="application/rss+xml"></atom:link><language>en</language><lastBuildDate>Fri, 21 Feb 2014 12:36:06 GMT</lastBuildDate><generator>Nikola &lt;http://getnikola.com/&gt;</generator><docs>http://blogs.law.harvard.edu/tech/rss</docs><item><title>Qualitative analysis and Bifurcation diagram Tutorial</title><link>http://mathbio.github.io/posts/qualitative-analysis-and-bifurcation-diagram-tutorial.html</link><description>&lt;div class="text_cell_render border-box-sizing rendered_html"&gt;
&lt;h1 id="qualitative-analysis-and-bifurcation-diagram-tutorial"&gt;Qualitative analysis and Bifurcation diagram Tutorial&lt;/h1&gt;
&lt;p&gt;&lt;em&gt;This tutorial assumes you have read the &lt;a href="http://nbviewer.ipython.org/github/diogro/ode_examples/blob/master/Numerical%20Integration%20Tutorial.ipynb?create=1"&gt;tutorial on numerical integration&lt;/a&gt;.&lt;/em&gt;&lt;/p&gt;
&lt;h2 id="exploring-the-parameter-space-bifurcation-diagrams"&gt;Exploring the parameter space: bifurcation diagrams&lt;/h2&gt;
&lt;h3 id="the-rosenzweig-macarthur-consumer-resource-model"&gt;The Rosenzweig-MacArthur consumer-resource model&lt;/h3&gt;
&lt;p&gt;&lt;span class="math"&gt;\[ \begin{aligned}
\frac{dR}{dt} &amp;amp;= rR \left( 1 - \frac{R}{K} \right) - \frac{a R C}{1+ahR} \\
\frac{dC}{dt} &amp;amp;= \frac{e a R C}{1+ahR} - d C
\end{aligned} \]&lt;/span&gt;&lt;/p&gt;
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&lt;h4 id="rosenzweigmacarthur-model-solutions"&gt;Rosenzweig–MacArthur model solutions&lt;/h4&gt;
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In [4]:
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&lt;div class="highlight"&gt;&lt;pre&gt;&lt;span class="o"&gt;%&lt;/span&gt;&lt;span class="k"&gt;matplotlib&lt;/span&gt; &lt;span class="n"&gt;inline&lt;/span&gt;
&lt;span class="kn"&gt;from&lt;/span&gt; &lt;span class="nn"&gt;numpy&lt;/span&gt; &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;
&lt;span class="kn"&gt;from&lt;/span&gt; &lt;span class="nn"&gt;scipy.integrate&lt;/span&gt; &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;odeint&lt;/span&gt;
&lt;span class="kn"&gt;from&lt;/span&gt; &lt;span class="nn"&gt;matplotlib.pyplot&lt;/span&gt; &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;
&lt;span class="n"&gt;ion&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;

&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;RM&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;r&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;K&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;e&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt; &lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt; &lt;span class="n"&gt;r&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="o"&gt;/&lt;/span&gt;&lt;span class="n"&gt;K&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="o"&gt;/&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;),&lt;/span&gt;
                   &lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;e&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="o"&gt;/&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;])&lt;/span&gt;

&lt;span class="n"&gt;t&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;arange&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1000&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;y0&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;1.&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
&lt;span class="n"&gt;pars&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt;  &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mf"&gt;1.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;10.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;1.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;0.1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;0.1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;0.1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="n"&gt;y&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;odeint&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;RM&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;y0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;pars&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;xlabel&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'time'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;ylabel&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'population'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;legend&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="s"&gt;'resource'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s"&gt;'consumer'&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;
&lt;/pre&gt;&lt;/div&gt;

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&lt;pre&gt;
&amp;lt;matplotlib.legend.Legend at 0x7f6646a77750&amp;gt;
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s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%0AQnRx/w8jmeFrDiJgXwAAAABJRU5ErkJggg=="&gt;

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&lt;h4 id="the-phase-space-flow-and-the-fixed-point"&gt;The phase space flow and the fixed point&lt;/h4&gt;
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In [18]:
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&lt;div class="highlight"&gt;&lt;pre&gt;&lt;span class="c"&gt;# plot the solution in the phase space&lt;/span&gt;
&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;[:,&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;[:,&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;
&lt;span class="c"&gt;# defines a grid of points&lt;/span&gt;
&lt;span class="n"&gt;R&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;C&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;meshgrid&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arange&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mf"&gt;0.95&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;1.25&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="mo"&gt;05&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="n"&gt;arange&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mf"&gt;0.95&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;1.04&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;0.01&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
&lt;span class="c"&gt;# calculates the value of the derivative at the point in the grid&lt;/span&gt;
&lt;span class="n"&gt;dy&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;RM&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="n"&gt;R&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;C&lt;/span&gt;&lt;span class="p"&gt;]),&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;pars&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="c"&gt;# plots arrows on the points of the grid, with the difection &lt;/span&gt;
&lt;span class="c"&gt;# and length determined by the derivative dy&lt;/span&gt;
&lt;span class="c"&gt;# This is a picture of the flow of the solution in the phase space&lt;/span&gt;
&lt;span class="n"&gt;quiver&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;R&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;C&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;dy&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,:],&lt;/span&gt; &lt;span class="n"&gt;dy&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,:],&lt;/span&gt; &lt;span class="n"&gt;scale_units&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="s"&gt;'xy'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;angles&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="s"&gt;'xy'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;xlabel&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'Resource'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;ylabel&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'Consumer'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/pre&gt;&lt;/div&gt;

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    Out[18]:&lt;/div&gt;
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&lt;pre&gt;
&amp;lt;matplotlib.text.Text at 0x7f6b393cc590&amp;gt;
&lt;/pre&gt;

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&lt;img 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q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"&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;/div&gt;
&lt;div class="text_cell_render border-box-sizing rendered_html"&gt;
&lt;h4 id="messing-a-little-with-the-parameters..."&gt;Messing a little with the parameters...&lt;/h4&gt;
&lt;/div&gt;
&lt;div class="cell border-box-sizing code_cell vbox"&gt;
&lt;div class="input hbox"&gt;
&lt;div class="prompt input_prompt"&gt;
In [5]:
&lt;/div&gt;
&lt;div class="input_area box-flex1"&gt;
&lt;div class="highlight"&gt;&lt;pre&gt;&lt;span class="c"&gt;# now K = 15&lt;/span&gt;
&lt;span class="n"&gt;t&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;arange&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1000&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;1.&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;pars&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt;  &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mf"&gt;1.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;15.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;1.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;0.1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;0.1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;0.1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;y_osc&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;odeint&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;RM&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;y0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;pars&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;y_osc&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;xlabel&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'time'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;ylabel&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'population'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;legend&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="s"&gt;'resource'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s"&gt;'consumer'&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;
&lt;/pre&gt;&lt;/div&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;div class="vbox output_wrapper"&gt;
&lt;div class="output vbox"&gt;


&lt;div class="hbox output_area"&gt;&lt;div class="prompt output_prompt"&gt;
    Out[5]:&lt;/div&gt;
&lt;div class="box-flex1 output_subarea output_pyout"&gt;


&lt;pre&gt;
&amp;lt;matplotlib.legend.Legend at 0x7f66633d4d50&amp;gt;
&lt;/pre&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;div class="hbox output_area"&gt;&lt;div class="prompt"&gt;&lt;/div&gt;
&lt;div class="box-flex1 output_subarea output_display_data"&gt;


&lt;img 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G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%0AhImzECZ5mzBhwsRZCJO8TZgwYeIsxP8HWv0sel5WJ7gAAAAASUVORK5CYII="&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;/div&gt;
&lt;div class="cell border-box-sizing code_cell vbox"&gt;
&lt;div class="input hbox"&gt;
&lt;div class="prompt input_prompt"&gt;
In [20]:
&lt;/div&gt;
&lt;div class="input_area box-flex1"&gt;
&lt;div class="highlight"&gt;&lt;pre&gt;&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;y_osc&lt;/span&gt;&lt;span class="p"&gt;[:,&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="n"&gt;y_osc&lt;/span&gt;&lt;span class="p"&gt;[:,&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;
&lt;span class="n"&gt;R&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;C&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;meshgrid&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arange&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;6.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="n"&gt;arange&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;2.1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;0.2&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
&lt;span class="n"&gt;dy&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;RM&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="n"&gt;R&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;C&lt;/span&gt;&lt;span class="p"&gt;]),&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;pars&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;quiver&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;R&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;C&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;dy&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,:],&lt;/span&gt; &lt;span class="n"&gt;dy&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,:],&lt;/span&gt; &lt;span class="n"&gt;scale_units&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="s"&gt;'xy'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;angles&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="s"&gt;'xy'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;xlabel&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'R'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;ylabel&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'C'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/pre&gt;&lt;/div&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;div class="vbox output_wrapper"&gt;
&lt;div class="output vbox"&gt;


&lt;div class="hbox output_area"&gt;&lt;div class="prompt output_prompt"&gt;
    Out[20]:&lt;/div&gt;
&lt;div class="box-flex1 output_subarea output_pyout"&gt;


&lt;pre&gt;
&amp;lt;matplotlib.text.Text at 0x7f6b3943dd90&amp;gt;
&lt;/pre&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;div class="hbox output_area"&gt;&lt;div class="prompt"&gt;&lt;/div&gt;
&lt;div class="box-flex1 output_subarea output_display_data"&gt;


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C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%0AhIo3hUKhOCH/H1DREy1Gjpu4AAAAAElFTkSuQmCC"&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;/div&gt;
&lt;div class="cell border-box-sizing code_cell vbox"&gt;
&lt;div class="input hbox"&gt;
&lt;div class="prompt input_prompt"&gt;
In [22]:
&lt;/div&gt;
&lt;div class="input_area box-flex1"&gt;
&lt;div class="highlight"&gt;&lt;pre&gt;&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mf"&gt;10.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;500&lt;/span&gt;&lt;span class="p"&gt;:,&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;min&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="s"&gt;'og'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mf"&gt;10.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;500&lt;/span&gt;&lt;span class="p"&gt;:,&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;max&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="s"&gt;'og'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mf"&gt;10.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;500&lt;/span&gt;&lt;span class="p"&gt;:,&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;min&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="s"&gt;'ob'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mf"&gt;10.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;500&lt;/span&gt;&lt;span class="p"&gt;:,&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;max&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="s"&gt;'ob'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mf"&gt;15.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;y_osc&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;500&lt;/span&gt;&lt;span class="p"&gt;:,&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;min&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="s"&gt;'og'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mf"&gt;15.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;y_osc&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;500&lt;/span&gt;&lt;span class="p"&gt;:,&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;max&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="s"&gt;'og'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mf"&gt;15.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;y_osc&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;500&lt;/span&gt;&lt;span class="p"&gt;:,&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;min&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="s"&gt;'ob'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mf"&gt;15.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;y_osc&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;500&lt;/span&gt;&lt;span class="p"&gt;:,&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;max&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="s"&gt;'ob'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;xlim&lt;/span&gt;&lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;20&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
&lt;span class="n"&gt;yscale&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'log'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;xlabel&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'K'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;ylabel&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'min / max population'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/pre&gt;&lt;/div&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;div class="vbox output_wrapper"&gt;
&lt;div class="output vbox"&gt;


&lt;div class="hbox output_area"&gt;&lt;div class="prompt output_prompt"&gt;
    Out[22]:&lt;/div&gt;
&lt;div class="box-flex1 output_subarea output_pyout"&gt;


&lt;pre&gt;
&amp;lt;matplotlib.text.Text at 0x7f6b3813d510&amp;gt;
&lt;/pre&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;div class="hbox output_area"&gt;&lt;div class="prompt"&gt;&lt;/div&gt;
&lt;div class="box-flex1 output_subarea output_display_data"&gt;


&lt;img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAXYAAAEOCAYAAACdLzzJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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%0AodgBwGb+H7AiYXSuzMy1AAAAAElFTkSuQmCC"&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;/div&gt;
&lt;div class="text_cell_render border-box-sizing rendered_html"&gt;
&lt;h3 id="the-paradox-of-enrichment"&gt;The paradox of enrichment&lt;/h3&gt;
&lt;p&gt;What happens when we change the carrying capacity &lt;span class="math"&gt;\(K\)&lt;/span&gt; from very small values up to very large values? For very small values, the resource is not going to sustain the consumer population, but for larger values ok &lt;span class="math"&gt;\(K\)&lt;/span&gt;, both species should be benefited... right?&lt;/p&gt;
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&lt;div class="cell border-box-sizing code_cell vbox"&gt;
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&lt;div class="prompt input_prompt"&gt;
In [9]:
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&lt;div class="highlight"&gt;&lt;pre&gt;&lt;span class="c"&gt;# empty lists to append the values later&lt;/span&gt;
&lt;span class="n"&gt;ymin&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[]&lt;/span&gt;
&lt;span class="n"&gt;ymax&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[]&lt;/span&gt;
&lt;span class="n"&gt;KK&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;arange&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;25&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;t&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;arange&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;6000&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;1.&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="c"&gt;# loop over the values of K (KK)&lt;/span&gt;
&lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;K&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;KK&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
    &lt;span class="c"&gt;# redefine the parameters using the new K&lt;/span&gt;
    &lt;span class="n"&gt;pars&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt;  &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mf"&gt;1.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;K&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;1.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;0.1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;0.1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;0.1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="c"&gt;# integrate again the equation, with new parameters&lt;/span&gt;
    &lt;span class="n"&gt;y&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;odeint&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;RM&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;y0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;pars&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="c"&gt;# calculate the minimum and maximum of the populations, but&lt;/span&gt;
    &lt;span class="c"&gt;# only for the last 1000 steps (the long-term solution),&lt;/span&gt;
    &lt;span class="c"&gt;# appending the result to the list&lt;/span&gt;
    &lt;span class="c"&gt;# question: is 1000 enough? When it wouldn't be?&lt;/span&gt;
    &lt;span class="n"&gt;ymin&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1000&lt;/span&gt;&lt;span class="p"&gt;:,:]&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;min&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;axis&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
    &lt;span class="n"&gt;ymax&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1000&lt;/span&gt;&lt;span class="p"&gt;:,:]&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;max&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;axis&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
&lt;span class="c"&gt;# convert the lists into arrays&lt;/span&gt;
&lt;span class="n"&gt;ymin&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ymin&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;ymax&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ymax&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="c"&gt;# and now, we plot the bifurcation diagram&lt;/span&gt;
&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;KK&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ymin&lt;/span&gt;&lt;span class="p"&gt;[:,&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="s"&gt;'g'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;KK&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ymax&lt;/span&gt;&lt;span class="p"&gt;[:,&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="s"&gt;'g'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;KK&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ymin&lt;/span&gt;&lt;span class="p"&gt;[:,&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="s"&gt;'b'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;KK&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ymax&lt;/span&gt;&lt;span class="p"&gt;[:,&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="s"&gt;'b'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;xlabel&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'$K$'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;ylabel&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'min/max populations'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;legend&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="s"&gt;'resource'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s"&gt;'consumer'&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;
&lt;span class="c"&gt;# use a log scale in the y-axis&lt;/span&gt;
&lt;span class="n"&gt;yscale&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'log'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/pre&gt;&lt;/div&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;div class="vbox output_wrapper"&gt;
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&lt;div class="hbox output_area"&gt;&lt;div class="prompt"&gt;&lt;/div&gt;
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b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%0ATkSkY5jYiYh0DBM7EZGO+X+kbp4RojrwQQAAAABJRU5ErkJggg=="&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;/div&gt;
&lt;div class="text_cell_render border-box-sizing rendered_html"&gt;
&lt;p&gt;Well, the first prediction was OK (notice that the plot above uses a log scale), but for high &lt;span class="math"&gt;\(K\)&lt;/span&gt;, the minima of the oscillation go to very low values, so that the populations have a high risk of extinction.&lt;/p&gt;
&lt;/div&gt;
&lt;div class="text_cell_render border-box-sizing rendered_html"&gt;
&lt;h3 id="consumer-resource-dynamics-in-a-seasonal-environment"&gt;Consumer-resource dynamics in a seasonal environment&lt;/h3&gt;
&lt;p&gt;&lt;span class="math"&gt;\[ \begin{aligned}
\frac{dR}{dt} &amp;amp;= r(t) R \left( 1 - \frac{R}{K} \right) - \frac{a R C}{1+ahR} \\
\frac{dC}{dt} &amp;amp;= \frac{e a R C}{1+ahR} - d C \\
r(t) &amp;amp;= r_0 (1+\alpha \sin(2\pi t/T))
\end{aligned} \]&lt;/span&gt;&lt;/p&gt;
&lt;/div&gt;
&lt;div class="cell border-box-sizing code_cell vbox"&gt;
&lt;div class="input hbox"&gt;
&lt;div class="prompt input_prompt"&gt;
In [6]:
&lt;/div&gt;
&lt;div class="input_area box-flex1"&gt;
&lt;div class="highlight"&gt;&lt;pre&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;RM_season&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;r&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;alpha&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;K&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;e&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="c"&gt;# in this function, `t` appears explicitly&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt; &lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt; &lt;span class="n"&gt;r&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="n"&gt;alpha&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;sin&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;pi&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="o"&gt;/&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;
                           &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="o"&gt;/&lt;/span&gt;&lt;span class="n"&gt;K&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="o"&gt;/&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;),&lt;/span&gt;
    &lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;e&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="o"&gt;/&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;])&lt;/span&gt;

&lt;span class="n"&gt;t&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;arange&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2000&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;1.&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;y0&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mf"&gt;1.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;1.&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
&lt;span class="n"&gt;pars&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt;  &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mf"&gt;1.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;0.1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;80.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;10.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;1.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;0.1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;0.1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;0.1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;y&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;odeint&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;RM_season&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;y0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;pars&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;xlabel&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'time'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;ylabel&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'population'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;legend&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="s"&gt;'resource'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s"&gt;'consumer'&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;
&lt;/pre&gt;&lt;/div&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;div class="vbox output_wrapper"&gt;
&lt;div class="output vbox"&gt;


&lt;div class="hbox output_area"&gt;&lt;div class="prompt output_prompt"&gt;
    Out[6]:&lt;/div&gt;
&lt;div class="box-flex1 output_subarea output_pyout"&gt;


&lt;pre&gt;
&amp;lt;matplotlib.legend.Legend at 0x7ff4c213ef10&amp;gt;
&lt;/pre&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;div class="hbox output_area"&gt;&lt;div class="prompt"&gt;&lt;/div&gt;
&lt;div class="box-flex1 output_subarea output_display_data"&gt;


&lt;img 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c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%0AgYSdQCAQ6gwk7AQCgVBn+P+vfVesHCg2IwAAAABJRU5ErkJggg=="&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;/div&gt;
&lt;div class="text_cell_render border-box-sizing rendered_html"&gt;
&lt;h4 id="a-resonance-diagram"&gt;A resonance diagram&lt;/h4&gt;
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&lt;div class="cell border-box-sizing code_cell vbox"&gt;
&lt;div class="input hbox"&gt;
&lt;div class="prompt input_prompt"&gt;
In [7]:
&lt;/div&gt;
&lt;div class="input_area box-flex1"&gt;
&lt;div class="highlight"&gt;&lt;pre&gt;&lt;span class="n"&gt;ymin&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[]&lt;/span&gt;
&lt;span class="n"&gt;ymax&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[]&lt;/span&gt;
&lt;span class="n"&gt;t&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;arange&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;6000&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;1.&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="c"&gt;# times&lt;/span&gt;
&lt;span class="n"&gt;TT&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;arange&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;80&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="c"&gt;# periods&lt;/span&gt;
&lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;T&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;TT&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
    &lt;span class="n"&gt;pars&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt;  &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mf"&gt;1.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;0.1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;T&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;10.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;1.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;0.1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;0.1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;0.1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="n"&gt;y&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;odeint&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;RM_season&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;y0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;pars&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="n"&gt;ymin&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1000&lt;/span&gt;&lt;span class="p"&gt;:,:]&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;min&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;axis&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
    &lt;span class="n"&gt;ymax&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1000&lt;/span&gt;&lt;span class="p"&gt;:,:]&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;max&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;axis&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
&lt;span class="n"&gt;ymin&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ymin&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;ymax&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ymax&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TT&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ymin&lt;/span&gt;&lt;span class="p"&gt;[:,&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="s"&gt;'g'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TT&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ymax&lt;/span&gt;&lt;span class="p"&gt;[:,&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="s"&gt;'g'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TT&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ymin&lt;/span&gt;&lt;span class="p"&gt;[:,&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="s"&gt;'b'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TT&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ymax&lt;/span&gt;&lt;span class="p"&gt;[:,&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="s"&gt;'b'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;xlabel&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'$T$'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;ylabel&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'min/max populations'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;legend&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="s"&gt;'resource'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s"&gt;'consumer'&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;
&lt;span class="n"&gt;yscale&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'log'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/pre&gt;&lt;/div&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;div class="vbox output_wrapper"&gt;
&lt;div class="output vbox"&gt;


&lt;div class="hbox output_area"&gt;&lt;div class="prompt"&gt;&lt;/div&gt;
&lt;div class="box-flex1 output_subarea output_display_data"&gt;


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L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"&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;/div&gt;
&lt;div class="text_cell_render border-box-sizing rendered_html"&gt;
&lt;h2 id="what-if-i-really-want-to-explore-a-10-dimensional-parameter-space"&gt;What if I really want to explore a 10-dimensional parameter space?&lt;/h2&gt;
&lt;p&gt;First: good luck. Second, you will probably have to sample the space, rather than go through the whole thing. The recommended method to do it is using so-called &lt;a href="http://en.wikipedia.org/wiki/Latin_hypercube_sampling"&gt;Latin Hypercube samples&lt;/a&gt;, that uses a random sampling while ensuring a roughly regularly-spaced distribution. There are implementations for both R and python:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;a href="http://cran.r-project.org/web/packages/pse/"&gt;R-Cran pse: Parameter space exploration&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href="http://pythonhosted.org/pyDOE/randomized.html"&gt;PyDOE: design of experiments for Python&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;/div&gt;</description><guid>http://mathbio.github.io/posts/qualitative-analysis-and-bifurcation-diagram-tutorial.html</guid><pubDate>Fri, 21 Feb 2014 15:36:04 GMT</pubDate></item><item><title>Numerical Integration Tutorial</title><link>http://mathbio.github.io/posts/numerical-integration-tutorial.html</link><description>&lt;div class="text_cell_render border-box-sizing rendered_html"&gt;
&lt;h1 id="numerically-solving-differential-equations-with-python"&gt;Numerically solving differential equations with python&lt;/h1&gt;
&lt;p&gt;&lt;em&gt;This is a brief description of what numerical integration is and a practical tutorial on how to do it in Python.&lt;/em&gt;&lt;/p&gt;
&lt;/div&gt;
&lt;div class="text_cell_render border-box-sizing rendered_html"&gt;
&lt;h2 id="software-required"&gt;Software required&lt;/h2&gt;
&lt;p&gt;&lt;em&gt;In order to run this notebook in your own computer, you need to install the following software:&lt;/em&gt;&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;&lt;a href="http://python.org"&gt;python&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href="http://numpy.org"&gt;numpy&lt;/a&gt; and &lt;a href="http://scipy.org"&gt;scipy&lt;/a&gt; - python scientific libraries&lt;/li&gt;
&lt;li&gt;&lt;a href="http://matplotlib.org"&gt;matplotlib&lt;/a&gt; - a library for plotting&lt;/li&gt;
&lt;li&gt;the &lt;a href="http://ipython.org/notebook.html"&gt;ipython notebook&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;On Windows and Mac, we recommend installing the &lt;a href="https://store.continuum.io/cshop/anaconda/"&gt;Anaconda distribution&lt;/a&gt;, which includes all of the above in a single package (among several other libraries), available at http://continuum.io/downloads.&lt;/p&gt;
&lt;p&gt;On Linux, you can install everything using your distribution's prefered way, e.g.:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;Debian/Ubuntu: &lt;code&gt;sudo apt-get install python-numpy python-scipy python-matplotlib python-ipython-notebook&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;Fedora: &lt;code&gt;sudo yum install python-numpy python-scipy python-matplotlib python-ipython-notebook&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;Arch: &lt;code&gt;sudo pacman -S python-numpy python-scipy python-matplotlib ipython python-tornado python-jinja&lt;/code&gt;&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;Code snippets shown here can also be copied into a pure text file with .py extension and ran outside the notebook (e.g., in an python or ipython shell).&lt;/p&gt;
&lt;h3 id="from-the-web"&gt;From the web&lt;/h3&gt;
&lt;p&gt;Alternatively, you can use a service that runs notebooks on the cloud, e.g. &lt;a href="https://cloud.sagemath.com/"&gt;SageMathCloud&lt;/a&gt; or &lt;a href="https://www.wakari.io/"&gt;wakari&lt;/a&gt;. It is possible to visualize publicly-available notebooks using http://nbviewer.ipython.org, but no computation can be performed (it just shows saved pre-calculated results).&lt;/p&gt;
&lt;/div&gt;
&lt;div class="text_cell_render border-box-sizing rendered_html"&gt;
&lt;h2 id="how-numerical-integration-works"&gt;How numerical integration works&lt;/h2&gt;
&lt;p&gt;Let's say we have a differential equation that we don't know how (or don't want) to derive its (analytical) solution. We can still find out what the solutions are through &lt;strong&gt;numerical integration&lt;/strong&gt;. So, how dows that work?&lt;/p&gt;
&lt;p&gt;The idea is to approximate the solution at successive small time intervals, extrapolating the value of the derivative over each interval. For example, let's take the differential equation&lt;/p&gt;
&lt;p&gt;&lt;span class="math"&gt;\[ \frac{dx}{dt} = f(x) = x (1 - x) \]&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;with an initial value &lt;span class="math"&gt;\(x_0 = 0.1\)&lt;/span&gt; at an initial time &lt;span class="math"&gt;\(t=0\)&lt;/span&gt; (that is, &lt;span class="math"&gt;\(x(0) = 0.1\)&lt;/span&gt;). At &lt;span class="math"&gt;\(t=0\)&lt;/span&gt;, the derivative &lt;span class="math"&gt;\(\frac{dx}{dt}\)&lt;/span&gt; values &lt;span class="math"&gt;\(f(0.1) = 0.1 \times (1-0.1) = 0.09\)&lt;/span&gt;. We pick a small interval step, say, &lt;span class="math"&gt;\(\Delta t = 0.5\)&lt;/span&gt;, and assume that that value of the derivative is a good approximation over the whole interval from &lt;span class="math"&gt;\(t=0\)&lt;/span&gt; up to &lt;span class="math"&gt;\(t=0.5\)&lt;/span&gt;. This means that in this time &lt;span class="math"&gt;\(x\)&lt;/span&gt; is going to increase by &lt;span class="math"&gt;\(\frac{dx}{dt} \times \Delta t = 0.09 \times 0.5 = 0.045\)&lt;/span&gt;. So our approximate solution for &lt;span class="math"&gt;\(x\)&lt;/span&gt; at &lt;span class="math"&gt;\(t=0.5\)&lt;/span&gt; is &lt;span class="math"&gt;\(x(0) + 0.045 = 0.145\)&lt;/span&gt;. We can then use this value of &lt;span class="math"&gt;\(x(0.5)\)&lt;/span&gt; to calculate the next point in time, &lt;span class="math"&gt;\(t=1\)&lt;/span&gt;. We calculate the derivative at each step, multiply by the time step and add to the previous value of the solution, as in the table below:&lt;/p&gt;
&lt;table&gt;
&lt;thead&gt;
&lt;tr class="header"&gt;
&lt;th align="right"&gt;&lt;span class="math"&gt;\(t\)&lt;/span&gt;&lt;/th&gt;
&lt;th align="right"&gt;&lt;span class="math"&gt;\(x\)&lt;/span&gt;&lt;/th&gt;
&lt;th align="right"&gt;&lt;span class="math"&gt;\(\frac{dx}{dt}\)&lt;/span&gt;&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr class="odd"&gt;
&lt;td align="right"&gt;0&lt;/td&gt;
&lt;td align="right"&gt;0.1&lt;/td&gt;
&lt;td align="right"&gt;0.09&lt;/td&gt;
&lt;/tr&gt;
&lt;tr class="even"&gt;
&lt;td align="right"&gt;0.5&lt;/td&gt;
&lt;td align="right"&gt;0.145&lt;/td&gt;
&lt;td align="right"&gt;0.123975&lt;/td&gt;
&lt;/tr&gt;
&lt;tr class="odd"&gt;
&lt;td align="right"&gt;1.0&lt;/td&gt;
&lt;td align="right"&gt;0.206987&lt;/td&gt;
&lt;td align="right"&gt;0.164144&lt;/td&gt;
&lt;/tr&gt;
&lt;tr class="even"&gt;
&lt;td align="right"&gt;1.5&lt;/td&gt;
&lt;td align="right"&gt;0.289059&lt;/td&gt;
&lt;td align="right"&gt;0.205504&lt;/td&gt;
&lt;/tr&gt;
&lt;tr class="odd"&gt;
&lt;td align="right"&gt;2.0&lt;/td&gt;
&lt;td align="right"&gt;0.391811&lt;/td&gt;
&lt;td align="right"&gt;0.238295&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;
&lt;p&gt;Of course, this is terribly tedious to do by hand, so we can write a simple program to do it and plot the solution. Below we compare it to the known analytical solution of this differential equation (the &lt;em&gt;logistic equation&lt;/em&gt;). &lt;strong&gt;Don't worry about the code just yet&lt;/strong&gt;: there are better and simpler ways to do it!&lt;/p&gt;
&lt;/div&gt;
&lt;div class="cell border-box-sizing code_cell vbox"&gt;
&lt;div class="input hbox"&gt;
&lt;div class="prompt input_prompt"&gt;
In [4]:
&lt;/div&gt;
&lt;div class="input_area box-flex1"&gt;
&lt;div class="highlight"&gt;&lt;pre&gt;&lt;span class="o"&gt;%&lt;/span&gt;&lt;span class="k"&gt;matplotlib&lt;/span&gt; &lt;span class="n"&gt;inline&lt;/span&gt;
&lt;span class="kn"&gt;from&lt;/span&gt; &lt;span class="nn"&gt;numpy&lt;/span&gt; &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;
&lt;span class="kn"&gt;from&lt;/span&gt; &lt;span class="nn"&gt;matplotlib.pyplot&lt;/span&gt; &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;

&lt;span class="c"&gt;# time intervals&lt;/span&gt;
&lt;span class="n"&gt;tt&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;arange&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;0.5&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="c"&gt;# initial condition&lt;/span&gt;
&lt;span class="n"&gt;xx&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mf"&gt;0.1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;

&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;f&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mf"&gt;1.&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="c"&gt;# loop over time&lt;/span&gt;
&lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;t&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;tt&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;:]:&lt;/span&gt;
    &lt;span class="n"&gt;xx&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;xx&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mf"&gt;0.5&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;f&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;xx&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]))&lt;/span&gt;

&lt;span class="c"&gt;# plotting&lt;/span&gt;
&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;tt&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;xx&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s"&gt;'.-'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;ta&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;arange&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;0.01&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ta&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;0.1&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;exp&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ta&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;/&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="mf"&gt;0.1&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;exp&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ta&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mf"&gt;1.&lt;/span&gt;&lt;span class="p"&gt;)))&lt;/span&gt;
&lt;span class="n"&gt;xlabel&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'t'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;ylabel&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'x'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;legend&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="s"&gt;'approximation'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s"&gt;'analytical solution'&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="n"&gt;loc&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="s"&gt;'best'&lt;/span&gt;&lt;span class="p"&gt;,)&lt;/span&gt;
&lt;/pre&gt;&lt;/div&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;div class="vbox output_wrapper"&gt;
&lt;div class="output vbox"&gt;


&lt;div class="hbox output_area"&gt;&lt;div class="prompt output_prompt"&gt;
    Out[4]:&lt;/div&gt;
&lt;div class="box-flex1 output_subarea output_pyout"&gt;


&lt;pre&gt;
&amp;lt;matplotlib.legend.Legend at 0x7ffd377a58d0&amp;gt;
&lt;/pre&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;div class="hbox output_area"&gt;&lt;div class="prompt"&gt;&lt;/div&gt;
&lt;div class="box-flex1 output_subarea output_display_data"&gt;


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A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"&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;/div&gt;
&lt;div class="text_cell_render border-box-sizing rendered_html"&gt;
&lt;h2 id="why-use-scientific-libraries"&gt;Why use scientific libraries?&lt;/h2&gt;
&lt;p&gt;The method we just used above is called the &lt;em&gt;Euler method&lt;/em&gt;, and is the simplest one available. The problem is that, although it works reasonably well for the differential equation above, in many cases it doesn't perform very well. There are many ways to improve it: in fact, there are many books entirely dedicated to this. Although many math or physics students do learn how to implement more sophisticated methods, the topic is really deep. Luckily, we can rely on the expertise of lots of people to come up with good algorithms that work well in most situations.&lt;/p&gt;
&lt;/div&gt;
&lt;div class="text_cell_render border-box-sizing rendered_html"&gt;
&lt;h2 id="then-how..."&gt;Then, how... ?&lt;/h2&gt;
&lt;p&gt;We are going to demonstrate how to use scientific libraries to integrate differential equations. Although the specific commands depend on the software, the general procedure is usually the same:&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;define the derivative function (the right hand side of the differential equation)&lt;/li&gt;
&lt;li&gt;choose a time step or a sequence of times where you want the solution&lt;/li&gt;
&lt;li&gt;provide the parameters and the initial condition&lt;/li&gt;
&lt;li&gt;pass the function, time sequence, parameters and initial conditions to a computer routine that runs the integration.&lt;/li&gt;
&lt;/ul&gt;
&lt;h3 id="a-single-equation"&gt;A single equation&lt;/h3&gt;
&lt;p&gt;So, let's start with the same equation as above, the logistic equation, now with any parameters for growth rate and carrying capacity:&lt;/p&gt;
&lt;p&gt;&lt;span class="math"&gt;\[ \frac{dx}{dt} = f(x) = r x \left(1 - \frac{x}{K} \right) \]&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;with &lt;span class="math"&gt;\(r=2\)&lt;/span&gt;, &lt;span class="math"&gt;\(K=10\)&lt;/span&gt; and &lt;span class="math"&gt;\(x(0) = 0.1\)&lt;/span&gt;. We show how to integrate it using python below, introducing key language syntax as necessary.&lt;/p&gt;
&lt;/div&gt;
&lt;div class="cell border-box-sizing code_cell vbox"&gt;
&lt;div class="input hbox"&gt;
&lt;div class="prompt input_prompt"&gt;
In [5]:
&lt;/div&gt;
&lt;div class="input_area box-flex1"&gt;
&lt;div class="highlight"&gt;&lt;pre&gt;&lt;span class="c"&gt;# everything after a '#' is a comment&lt;/span&gt;

&lt;span class="c"&gt;## we begin importing libraries we are going to use&lt;/span&gt;
&lt;span class="c"&gt;# import all (*) functions from numpy library, eg array, arange etc.&lt;/span&gt;
&lt;span class="kn"&gt;from&lt;/span&gt; &lt;span class="nn"&gt;numpy&lt;/span&gt; &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;
&lt;span class="c"&gt;# import all (*) interactive plotting functions, eg plot, xlabel etc.&lt;/span&gt;
&lt;span class="kn"&gt;from&lt;/span&gt; &lt;span class="nn"&gt;matplotlib.pyplot&lt;/span&gt; &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;
&lt;span class="c"&gt;# import the numerical integrator we will use, odeint()&lt;/span&gt;
&lt;span class="kn"&gt;from&lt;/span&gt; &lt;span class="nn"&gt;scipy.integrate&lt;/span&gt; &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;odeint&lt;/span&gt;

&lt;span class="c"&gt;# time steps: an array of values starting from 0 going up to (but&lt;/span&gt;
&lt;span class="c"&gt;# excluding) 10, in steps of 0.01&lt;/span&gt;
&lt;span class="n"&gt;t&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;arange&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;10.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;0.01&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="c"&gt;# parameters&lt;/span&gt;
&lt;span class="n"&gt;r&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mf"&gt;2.&lt;/span&gt;
&lt;span class="n"&gt;K&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mf"&gt;10.&lt;/span&gt;
&lt;span class="c"&gt;# initial condition&lt;/span&gt;
&lt;span class="n"&gt;x0&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mf"&gt;0.1&lt;/span&gt;

&lt;span class="c"&gt;# let's define the right-hand side of the differential equation&lt;/span&gt;
&lt;span class="c"&gt;# It must be a function of the dependent variable (x) and of the &lt;/span&gt;
&lt;span class="c"&gt;# time (t), even if time does not appear explicitly&lt;/span&gt;
&lt;span class="c"&gt;# this is how you define a function:&lt;/span&gt;
&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;f&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;r&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;K&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="c"&gt;# in python, there are no curling braces '{}' to start or &lt;/span&gt;
    &lt;span class="c"&gt;# end a function, nor any special keyword: the block is defined&lt;/span&gt;
    &lt;span class="c"&gt;# by leading spaces (usually 4)&lt;/span&gt;
    &lt;span class="c"&gt;# arithmetic is done the same as in other languages: + - * /&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;r&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="o"&gt;/&lt;/span&gt;&lt;span class="n"&gt;K&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="c"&gt;# call the function that performs the integration&lt;/span&gt;
&lt;span class="c"&gt;# the order of the arguments is as below: the derivative function,&lt;/span&gt;
&lt;span class="c"&gt;# the initial condition, the points where we want the solution, and&lt;/span&gt;
&lt;span class="c"&gt;# a list of parameters&lt;/span&gt;
&lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;odeint&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;f&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;x0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;r&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;K&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;

&lt;span class="c"&gt;# plot the solution&lt;/span&gt;
&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;xlabel&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'t'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="c"&gt;# define label of x-axis&lt;/span&gt;
&lt;span class="n"&gt;ylabel&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'x'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="c"&gt;# and of y-axis&lt;/span&gt;

&lt;span class="c"&gt;# plot analytical solution&lt;/span&gt;
&lt;span class="c"&gt;# notice that `t` is an array: when you do any arithmetical operation&lt;/span&gt;
&lt;span class="c"&gt;# with an array, it is the same as doing it for each element&lt;/span&gt;
&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;K&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;x0&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;exp&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;r&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;/&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;K&lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="n"&gt;x0&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;exp&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;r&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mf"&gt;1.&lt;/span&gt;&lt;span class="p"&gt;)))&lt;/span&gt;
&lt;span class="n"&gt;legend&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="s"&gt;'approximation'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s"&gt;'analytical solution'&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="n"&gt;loc&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="s"&gt;'best'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="c"&gt;# draw legend&lt;/span&gt;
&lt;/pre&gt;&lt;/div&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;div class="vbox output_wrapper"&gt;
&lt;div class="output vbox"&gt;


&lt;div class="hbox output_area"&gt;&lt;div class="prompt output_prompt"&gt;
    Out[5]:&lt;/div&gt;
&lt;div class="box-flex1 output_subarea output_pyout"&gt;


&lt;pre&gt;
&amp;lt;matplotlib.legend.Legend at 0x7ffd12020050&amp;gt;
&lt;/pre&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;div class="hbox output_area"&gt;&lt;div class="prompt"&gt;&lt;/div&gt;
&lt;div class="box-flex1 output_subarea output_display_data"&gt;


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3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"&gt;

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&lt;p&gt;We get a much better approximation now, the two curves superimpose each other!&lt;/p&gt;
&lt;p&gt;Now, what if we wanted to integrate a system of differential equations? Let's take the Lotka-Volterra equations:&lt;/p&gt;
&lt;p&gt;&lt;span class="math"&gt;\[ \begin{aligned}
\frac{dV}{dt} &amp;amp;= r V - c V P\\
\frac{dP}{dt} &amp;amp;= ec V P - dP
\end{aligned}\]&lt;/span&gt;&lt;/p&gt;
&lt;p&gt;In this case, the variable is no longer a number, but an array &lt;code&gt;[V, P]&lt;/code&gt;. We do the same as before, but now &lt;code&gt;x&lt;/code&gt; is going to be an array:&lt;/p&gt;
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In [8]:
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&lt;div class="highlight"&gt;&lt;pre&gt;&lt;span class="c"&gt;# we didn't need to do this again: if the cell above was run already,&lt;/span&gt;
&lt;span class="c"&gt;# the libraries are imported, but we repeat it here for convenience&lt;/span&gt;
&lt;span class="kn"&gt;from&lt;/span&gt; &lt;span class="nn"&gt;numpy&lt;/span&gt; &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;
&lt;span class="kn"&gt;from&lt;/span&gt; &lt;span class="nn"&gt;matplotlib.pyplot&lt;/span&gt; &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;
&lt;span class="kn"&gt;from&lt;/span&gt; &lt;span class="nn"&gt;scipy.integrate&lt;/span&gt; &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;odeint&lt;/span&gt;

&lt;span class="n"&gt;t&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;arange&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;50.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;0.01&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="c"&gt;# parameters&lt;/span&gt;
&lt;span class="n"&gt;r&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mf"&gt;2.&lt;/span&gt;
&lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mf"&gt;0.5&lt;/span&gt;
&lt;span class="n"&gt;e&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mf"&gt;0.1&lt;/span&gt;
&lt;span class="n"&gt;d&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mf"&gt;1.&lt;/span&gt;

&lt;span class="c"&gt;# initial condition: this is an array now!&lt;/span&gt;
&lt;span class="n"&gt;x0&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="mf"&gt;1.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;3.&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;

&lt;span class="c"&gt;# the function still receives only `x`, but it will be an array, not a number&lt;/span&gt;
&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;LV&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;r&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;e&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="c"&gt;# in python, arrays are numbered from 0, so the first element &lt;/span&gt;
    &lt;span class="c"&gt;# is x[0], the second is x[1]. The square brackets `[ ]` define a&lt;/span&gt;
    &lt;span class="c"&gt;# list, that is converted to an array using the function `array()`.&lt;/span&gt;
    &lt;span class="c"&gt;# Notice that the first entry corresponds to dV/dt and the second to dP/dt&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt; &lt;span class="n"&gt;r&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
                   &lt;span class="n"&gt;e&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;d&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="p"&gt;])&lt;/span&gt;

&lt;span class="c"&gt;# call the function that performs the integration&lt;/span&gt;
&lt;span class="c"&gt;# the order of the arguments is as below: the derivative function,&lt;/span&gt;
&lt;span class="c"&gt;# the initial condition, the points where we want the solution, and&lt;/span&gt;
&lt;span class="c"&gt;# a list of parameters&lt;/span&gt;
&lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;odeint&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;LV&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;x0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;r&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;e&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;

&lt;span class="n"&gt;VV&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;arange&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mf"&gt;0.1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;1.&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mf"&gt;0.01&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="k"&gt;for&lt;/span&gt; 

&lt;span class="c"&gt;# Now `x` is a 2-dimension array of size 5000 x 2 (5000 time steps by 2&lt;/span&gt;
&lt;span class="c"&gt;# variables). We can check it like this:&lt;/span&gt;
&lt;span class="k"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'shape of x:'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;shape&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="c"&gt;# plot the solution&lt;/span&gt;
&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;xlabel&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'t'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="c"&gt;# define label of x-axis&lt;/span&gt;
&lt;span class="n"&gt;ylabel&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'populations'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="c"&gt;# and of y-axis&lt;/span&gt;
&lt;span class="n"&gt;legend&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="s"&gt;'V'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s"&gt;'P'&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="n"&gt;loc&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="s"&gt;'upper right'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/pre&gt;&lt;/div&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;div class="vbox output_wrapper"&gt;
&lt;div class="output vbox"&gt;


&lt;div class="hbox output_area"&gt;&lt;div class="prompt"&gt;&lt;/div&gt;
&lt;div class="box-flex1 output_subarea output_stream output_stdout"&gt;
&lt;pre&gt;
shape of x: (5000, 2)

&lt;/pre&gt;
&lt;/div&gt;
&lt;/div&gt;

&lt;div class="hbox output_area"&gt;&lt;div class="prompt output_prompt"&gt;
    Out[8]:&lt;/div&gt;
&lt;div class="box-flex1 output_subarea output_pyout"&gt;


&lt;pre&gt;
&amp;lt;matplotlib.legend.Legend at 0x7ffd11f45850&amp;gt;
&lt;/pre&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;div class="hbox output_area"&gt;&lt;div class="prompt"&gt;&lt;/div&gt;
&lt;div class="box-flex1 output_subarea output_display_data"&gt;


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o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%0AICAg4Ab4/z9YY7mpI+ehAAAAAElFTkSuQmCC"&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;/div&gt;
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&lt;div class="text_cell_render border-box-sizing rendered_html"&gt;
&lt;p&gt;An interesting thing to do here is take a look at the &lt;em&gt;phase space&lt;/em&gt;, that is, plot only the dependent variables, without respect to time:&lt;/p&gt;
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In [9]:
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&lt;div class="highlight"&gt;&lt;pre&gt;&lt;span class="c"&gt;# `x[0,0]` is the first value (1st line, 1st column), `x[0,1]` is the value of &lt;/span&gt;
&lt;span class="c"&gt;# the 1st line, 2nd column, which corresponds to the value of P at the initial&lt;/span&gt;
&lt;span class="c"&gt;# time. We plot just this point first to know where we started:&lt;/span&gt;
&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="s"&gt;'o'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="k"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'Initial condition:'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;

&lt;span class="c"&gt;# `x[0]` or (equivalently) x[0,:] is the first line, and `x[:,0]` is the first&lt;/span&gt;
&lt;span class="c"&gt;# column. Notice the colon `:` stands for all the values of that axis. We are&lt;/span&gt;
&lt;span class="c"&gt;# going to plot the second column (P) against the first (V):&lt;/span&gt;
&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;[:,&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;[:,&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;
&lt;span class="n"&gt;plot&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="p"&gt;[:,&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="n"&gt;x2&lt;/span&gt;&lt;span class="p"&gt;[:,&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;
&lt;span class="n"&gt;xlabel&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'V'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;ylabel&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;'P'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/pre&gt;&lt;/div&gt;

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&lt;pre&gt;
Initial condition: [ 1.  3.]

&lt;/pre&gt;
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    Out[9]:&lt;/div&gt;
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&lt;pre&gt;
&amp;lt;matplotlib.text.Text at 0x7ffd11e70ad0&amp;gt;
&lt;/pre&gt;

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&lt;img 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k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"&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;/div&gt;
&lt;/div&gt;

&lt;/div&gt;
&lt;div class="text_cell_render border-box-sizing rendered_html"&gt;
&lt;p&gt;&lt;strong&gt;Congratulations&lt;/strong&gt;: you are now ready to integrate any system of differential equations! (We hope generalizing the above to more than 2 equations won't be very challenging).&lt;/p&gt;
&lt;/div&gt;
&lt;div class="text_cell_render border-box-sizing rendered_html"&gt;
&lt;h3 id="for-more-info"&gt;For more info:&lt;/h3&gt;
&lt;ul&gt;
&lt;li&gt;&lt;a href="http://docs.python.org/3/tutorial/index.html"&gt;Python tutorial&lt;/a&gt; (chapters 3 to 5 are specially useful).&lt;/li&gt;
&lt;li&gt;&lt;a href="http://nbviewer.ipython.org/github/iguananaut/notebooks/blob/master/numpy.ipynb"&gt;An introduction to Numpy&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href="http://nbviewer.ipython.org/github/jrjohansson/scientific-python-lectures/blob/master/Lecture-2-Numpy.ipynb"&gt;Another one&lt;/a&gt;, covering a little bit more ground.&lt;/li&gt;
&lt;li&gt;&lt;a href="http://matplotlib.org/gallery.html"&gt;The matplotlib gallery&lt;/a&gt;: all kinds of plots, with sample code to use.&lt;/li&gt;
&lt;/ul&gt;
&lt;/div&gt;</description><guid>http://mathbio.github.io/posts/numerical-integration-tutorial.html</guid><pubDate>Fri, 21 Feb 2014 05:02:20 GMT</pubDate></item><item><title>From Consumer-Resource to single-species dynamics</title><link>http://mathbio.github.io/posts/from-consumer-resource-to-single-species-dynamics.html</link><description>&lt;div class="text_cell_render border-box-sizing rendered_html"&gt;
&lt;h3 id="from-consumer-resource-models-to-single-species-dynamics"&gt;From consumer-resource models to single-species dynamics&lt;/h3&gt;
&lt;p&gt;We are interested in building simple consumer-resource models and exploring how single-species models emerge as we simplify the dynamics of the resource. We assume a simple Lotka-Volterra type equation, with a carrying capacity for the resource: &lt;/p&gt;&lt;p class="more"&gt;&lt;a href="http://mathbio.github.io/posts/from-consumer-resource-to-single-species-dynamics.html"&gt;Read more&lt;/a&gt;&lt;/p&gt;&lt;/div&gt;</description><category>consumer resource</category><category>single species</category><category>dynamics</category><guid>http://mathbio.github.io/posts/from-consumer-resource-to-single-species-dynamics.html</guid><pubDate>Wed, 19 Feb 2014 03:07:55 GMT</pubDate></item></channel></rss>