hypersynchronization.order_parameter

hypersynchronization.order_parameter(thetas, order=1, complex=False, axis=0)

Calculate the generalised Daido order parameter of order order.

The order parameter is a measure of how the phase angles are aligned. It can be used to quantify the level of synchronization or coherence in a system.

Parameters:

thetasarray-like, shape (n_oscillators,) or (n_oscillators, n_times)

Phases of the oscillators over time.

orderint, optional

The order of the order parameter. Default is 1.

complexbool, optional

If True, return the complex order parameter. If False (default), return its magnitude.

axisint, optional

The axis of length n_oscillators, along which the sum of the phases is taken. Default is 0.

Returns:

resultfloat or numpy.ndarray

If complex is True, the complex order parameter. If complex is False, the magnitude of the order parameter.

See also

identify_state

Identify the overall synchronization state.

Examples

>>> import numpy as np
>>> import hypersynchronization as hs
>>> theta = np.zeros(10)  # fully synchronized
>>> hs.order_parameter(theta)
1.0
>>> theta = np.linspace(0, 2 * np.pi, 10, endpoint=False)  # splay state
>>> np.isclose(hs.order_parameter(theta), 0)
True