DelayedKuramotoCoupling

experimental.network_dynamics.coupling.DelayedKuramotoCoupling(
    buffer_strategy='roll',
    warn_on_delay_clamp=False,
    history_interpolation=None,
    **kwargs,
)

Phase-difference coupling for Kuramoto oscillators with transmission delays.

Implements the delayed Kuramoto interaction:

\[c_i(t) = G \cdot \sum_{j} w_{ij} \sin(\theta_j(t - \tau_{ij}) - \theta_i(t))\]

where \(\tau_{ij}\) are the transmission delays between nodes. This is the standard model used to study delay-induced (de)synchronization, e.g. the two-oscillator multistability of Yeung & Strogatz (1999) and the conduction-speed-dependent synchronization resonances of Petkoski & Jirsa (2019) on brain networks.

Parameters

Name	Type	Description	Default
source	str or list of str	State name(s) to collect from connected nodes (typically 'theta')	required
local	str or list of str	State name(s) from current node (required for the phase difference)	required

Attributes

Name	Type	Description
N_OUTPUT_STATES	int	Number of output coupling states: 1
DEFAULT_PARAMS	Bunch	Default parameters: G=1.0 (global coupling strength)

Notes

G is not normalized by network size or degree; scale it (e.g. G/N) to match a particular Kuramoto convention.

Examples

>>> coupling = DelayedKuramotoCoupling(source='theta', local='theta', G=1.0)

References

Yeung, M. K. S., & Strogatz, S. H. (1999). Time delay in the Kuramoto model of coupled oscillators. Physical Review Letters, 82(3), 648.

Petkoski, S., & Jirsa, V. K. (2019). Transmission time delays organize the brain network synchronization. Philosophical Transactions of the Royal Society A, 377(2153), 20180132.

Methods

Name	Description
post	Apply coupling strength to summed delayed phase interactions.
pre	Compute sin(theta_j(t - tau) - theta_i(t)) per edge.

post

experimental.network_dynamics.coupling.DelayedKuramotoCoupling.post(
    summed_inputs,
    local_states,
    params,
)

Apply coupling strength to summed delayed phase interactions.

Args: summed_inputs: Summed delayed sin(theta_j - theta_i) terms [n_inputs, n_nodes] local_states: Local states (not used) params: Bunch with G

Returns: Scaled coupling [n_inputs, n_nodes]

pre

experimental.network_dynamics.coupling.DelayedKuramotoCoupling.pre(
    delayed_states,
    local_states,
    params,
)

Compute sin(theta_j(t - tau) - theta_i(t)) per edge.

Args: delayed_states: Delayed source phases [n_incoming, *M]. local_states: Current target phases aligned as [n_local, *M]. params: Coupling parameters (not used in pre)

Returns: Delayed phase-difference sine [n_output, *M].