Requirements

Following packages are required:

• numpy v1.11.0 or newer
• scipy v0.17 or newer

Installation

Via pip: `(sudo) pip install classify_chimeras`

Via source: https://github.com/fkemeth/classify_chimeras

Documentation

This python package contains functions to classify chimera states, non-linear hybrid states of coexisting coherence and incoherence. In partical, this package offers three functions, following the paper "A classification scheme for chimera states" (http://dx.doi.org/10.1063/1.4959804)

• `spatial(A, boundaries='no-flux', phases=False, nbins=100)` `A` 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(A, nbins=100, phases=False, Ncoarse=1500)` `A` 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 `A` contains phases only. `Ncoarse` 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(A, nbins=100, phases=False, Ncoarse=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 `A` contains phases only. `Ncoarse` 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.

Example

As an illustrative example, we use a chimera 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 classify_chimeras as clc
import pylab as pl

# Plot a snapshot of the data matrix A
(T,N) = A.shape
pl.plot(np.arange(0,1,1.0/float(N)),A[-1],'.'); pl.show()


# Obtain the fraction of spatially coherent oscillators
g0 = clc.spatial(A, boundaries='periodic', phases=True)
pl.plot(g0); pl.ylim((0,1.0)); pl.show()


# Obtain the fraction of temporarily correlated oscillators
h = clc.temporal(A, phases=True)
pl.plot(h); pl.ylim((0,0.3)); pl.show()
h0 = np.sqrt(h[-1])


Licence

This work is licenced under GNU General Public License v3. This means you must 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.