Package: classify-chimeras
INSTALLATIONVia pip:pip install classify_chimerasVia sourcegit clone https://github.com/fkemeth/classify_chimeras
cd classify_chimeras
pip install .DOCUMENTATIONThis 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)datamust be a TxN or a TxN1xN2 numpy matrix (either real or complex).
The functionspatial()applies the discrete Laplacian on the data, and returns the coherent
fraction at each time step.boundariesspecifies the boundary conditions under which the data was
generated. Setphases=Trueif A contains phases only.nbinsspecifies the number of bins of the histograms
which are generated.globaldist(data, nbins=100, phases=False, num_coarse=1500)datamust be a TxN numpy matrix.
The functionglobaldist()calculates all pariwise Euclidean distances between all data points at
each time step, and returns
the coherent fraction of A at each time step.nbinsspecifies the number of bins of the histograms.
Setphases=Trueifdatacontains phases only.num_coarseis 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 functiontemporal()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.nbinsspecifies the number of bins of the histograms.
Setphases=Trueifdatacontains phases only.num_coarseis 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.ISSUESFor questions, please contact (felix@kemeth.de), or visitthe GitHub repo.EXAMPLEAs 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.2.0.0Refactored 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.LICENCEThis 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.