A Matlab Toolbox for the Simulation, Analysis, and Design of Continuous Dynamical Systems Based on Networks of Stable Heteroclinic Channels (SHCs).
NOTICE: Code for Designing Responsive Pattern Generators: Stable Heteroclinic Channel Cycles for Modeling and Control by Horchler, et al. (2015) can be found here.
How to install (and uninstall) SHCTools:
- Download and expand the SHCTools-master.zip ZIP archive of the repository.
- Move the resultant SHCTools-master folder to the desired permanent location.
- In Matlab, navigate to SHCTools-master/SHCTools/ and run
shc_install. This adds the necessary files and folders to the Matlab search path. To uninstall SHCTools, runshc_install('remove'). - Minor edits and bug reports and fixes can be submitted by filing an issue or via email. To add new functionality or make propose major changes, please fork the repository. Any new features should be accompanied by some means of testing. Email or file an issue if you have any questions.
Lotka-Volterra SHC network tools.
shc_lv_createcycle - Create Lotka-Volterra SHC cycle from parameters.
shc_lv_eigs - Eigenvalues/vectors of Lotka-Volterra system.
shc_lv_epsilonfit - Nonlinear-compensated (fitted) noise magnitude.
shc_lv_equilibria - Solve for all equlibrium points symbolically.
shc_lv_ic - Generate initial conditions on the SHC manifold.
shc_lv_integrate - Solve Lotka-Volterra SDEs numerically.
shc_lv_iscycle - Check if Lotka-Volterra system is an SHC cycle.
shc_lv_isstable - Check stability of Lotka-Volterra system nodes.
shc_lv_isuniform - Check if Lotka-Volterra system is uniform SHC.
shc_lv_jacobian - Jacobian of N-dimensional Lotka-Volterra system.
shc_lv_lambda_us - Dominant unstable and stable eigenvalues.
shc_lv_meanperiod - Simulate system to find average mean period.
shc_lv_mintransitiontime - Estimate minimum transition times of network.
shc_lv_neighborhood - Scaled neighborhood-size for Lotka-Volterra SHC.
shc_lv_ode - ODEs for N-dimensional Lotka-Volterra system.
shc_lv_params - Find RHO matrix parameters from description.
shc_lv_passagetime - Mean first passage times of SHC network.
shc_lv_stability - Saddle values of Lotka-Volterra system nodes.
shc_lv_symparams - Create symbolic SHC parameters with assumptions.
shc_lv_taufit - Nonlinear-compensated (fitted) mean period.
Stone-Holmes distribution.
stoneholmescdf - Cummulative distribution function.
stoneholmeschi2gof - Chi-squared goodness-of-fit test.
stoneholmesdemo - Demonstrate Stone-Holmes distribution functions.
stoneholmesfit - Parameter estimates from data.
stoneholmesinv - Inverse cummulative distribution.
stoneholmesinvpassagetime - Noise as a function of mean passage time.
stoneholmesksdensity - Kernel density estimation for distribution.
stoneholmeskstest - Kolmogorov-Smirnov goodness-of-fit test.
stoneholmeslike - Negative log-likelihood.
stoneholmesmedian - Median of distribution.
stoneholmesmode - Mode (maximum value) of distribution.
stoneholmespassagetime - Mean passage time.
stoneholmespdf - Probability density function.
stoneholmesrnd - Random number generator.
stoneholmesstat - Mean and variance of distribution.
stoneholmesvar - Variance of Stone-Holmes distribution samples.
References
- V.S. Afraimovich, M.I. Rabinovich, and P. Varona, “Heteroclinic contours in neural ensembles and the winnerless competition principle,” Int. J. Bifurcation Chaos, Vol. 14, 2004, pp. 1195–1208. [PDF Preprint] [http://dx.doi.org/10.1142/S0218127404009806]
- A.D. Horchler, K.A. Daltorio, H.J. Chiel, and R.D Quinn “Designing Responsive Pattern Generators: Stable Heteroclinic Channel Cycles for Modeling and Control,” Bioinspir. Biomim., Vol. 10, No. 2, 2015, pp. 1–16. [http://dx.doi.org/10.1088/1748-3190/10/2/026001] (Please contact me for a copy of the manuscript.)
- M.I. Rabinovich, R. Huerta, P. Varona, and V.S. Afraimovich, “Transient Cognitive Dynamics, Metastability, and Decision Making,” PLoS Comp. Biol., Vol. 4, No. 5, 2008, e1000072. [http://dx.doi.org/10.1371/journal.pcbi.1000072]
- J.W. Reyn, “A Stability Criterion for Separatrix Polygons in the Phase Plane,” Nieuw Archief Voor Wiskunde (3), Vol. 27, 1979, pp. 238–254. [PDF]
- K.M. Shaw, Y.-M. Park, H.J. Chiel, and P.J. Thomas, “Phase Resetting in an Asymptotically Phaseless System: On the Phase Response of Limit Cycles Verging on a Heteroclinic Orbit,” SIAM J. Appl. Dyn. Syst., Vol. 11, No. 1, 2012, pp. 350–391. [http://dx.doi.org/10.1137/110828976]
- E. Stone and P. Holmes, “Random Perturbations of Heteroclinic Attractors,” SIAM J. Appl. Math., Vol. 50, No. 3, 1990, pp. 726–743. [http://jstor.org/stable/2101884]
Andrew D. Horchler, horchler @ gmail . com, biorobots.case.edu
Created: 1-4-12, Version: 1.3, 4-5-14
This version tested with Matlab 8.5.0.173394 (R2015a)
Mac OS X 10.10.2 (Build: 14C1514), Java 1.7.0_60-b19
Compatibility maintained back through Matlab 7.4 (R2007a)
Acknowledgment of support: This material is based upon work supported by the National Science Foundation under Grant No. 1065489. Disclaimer: Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
Copyright © 2012–2017, Andrew D. Horchler
All rights reserved.
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- Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
- Neither the name of Case Western Reserve University nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.
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