Chimera states in nonlocally-coupled phase oscillators
Project description
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 functionspatial()
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. Setphases=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 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.nbins
specifies the number of bins of the histograms. Setphases=True
ifA
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 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.nbins
specifies the number of bins of the histograms. Setphases=True
ifA
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.
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()
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.
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