INSTALLATION

Via pip:

pip install classify_chimeras

Via source

git clone https://github.com/fkemeth/classify_chimeras
cd classify_chimeras
pip install .

DOCUMENTATION

This python package contains functions to classify chimera states, non-linear hybrid states of coexisting coherence and incoherence. In particular, this package offers three functions, following the paper

"A classification scheme for chimera states" (http://dx.doi.org/10.1063/1.4959804)

• spatial(data, boundaries='no-flux', phases=False, nbins=100) data must be a TxN or a TxN1xN2 numpy matrix (either real or complex). The function spatial() applies the discrete Laplacian on the data, and returns the coherent fraction at each time step. boundaries specifies the boundary conditions under which the data was generated. Set phases=True if A contains phases only. nbins specifies the number of bins of the histograms which are generated.
• globaldist(data, nbins=100, phases=False, num_coarse=1500) data must be a TxN numpy matrix. The function globaldist() calculates all pariwise Euclidean distances between all data points at each time step, and returns the coherent fraction of A at each time step. nbins specifies the number of bins of the histograms. Set phases=True if data contains phases only. num_coarse is a threshold above which the data is coarsed due to memory limitations. This can be increased, but may lead to long calculation times or memory errors.
• temporal(data, nbins=100, phases=False, num_coarse=1500) A must be a TxN or TxN1xN2 numpy matrix. The function temporal() calculates all pairwise temporal correlation coefficients between the T-long timeseries of A. It returns a hisogram, with the square root of the last bin indicating the amount of temporarily correlated time series. nbins specifies the number of bins of the histograms. Set phases=True if data contains phases only. num_coarse is a threshold above which the data is coarsed due to memory limitations. This can be increased, but may lead to long calculation times or memory errors.

ISSUES

For questions, please contact (felix@kemeth.de), or visit the GitHub repo.

EXAMPLE

As an illustrative example, we use a chimer state observed by Kuramoto and Battogtokh in "Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators" (2002), in Nonlinear Phenom. Complex Syst. We suppose that we have the phases of this chimera state in a numpy matrix A.

import matplotlib.pyplot as plt

from kuramoto_chimera import integrate
from classify_chimeras import spatial, temporal

# Integrate Kuramoto phase oscillator system with nonlocal coupling.
data_dict = integrate()

# Plot a snapshot of the data matrix A

fig = plt.figure()
ax = fig.add_subplot(111)
ax.scatter(data_dict["xx"], data_dict["data"][-1])
ax.set_xlabel('x')
plt.show()

# Obtain the fraction of spatially coherent oscillators
g_zero = spatial(data_dict["data"], boundaries='periodic', phases=True)

fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(data_dict["t_eval"], g_zero)
ax.set_xlabel('t')
ax.set_ylim((0, 1.0))
plt.show()

# Obtain the fraction of temporarily correlated oscillators
temporal_coherence = temporal(data_dict["data"], phases=True)

fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(temporal_coherence)
ax.set_ylim((0, 0.3))
plt.show()

Changelog v.2.0.0

• Refactored code for the correlation measures.
• Restructured code to confirm to pypi package layout.
• Use random subset of grid points when coarse graining data.
• Adjusted upper bound in temporal correlation histogram to 1+epsilon.
• Included example using kuramoto_chimera package.
• Added notebook example.
• Added unit tests.

LICENCE

This work is licenced under GNU General Public License v3. Please cite

"A classification scheme for chimera states" F.P. Kemeth et al. (http://dx.doi.org/10.1063/1.4959804)

if you use this package for publications.