Spatio-temporal dynamics of Kuramoto-Sakaguchi model with time dependent connectivity

TL;DR

This paper investigates the spatio-temporal behavior of the Kuramoto-Sakaguchi model with time-dependent connectivity, revealing how collective states evolve, exhibit hysteresis, and depend on the relative time-scales of coupling changes.

Contribution

It introduces a detailed analysis of the Kuramoto-Sakaguchi model with dynamic connectivity, combining numerical simulations and Ott-Antonsen theory to uncover new dynamical states and time-scale effects.

Findings

System relaxes between states during quasi-static coupling changes

Global order parameter shows hysteresis with sinusoidal coupling variation

Distinct behaviors emerge depending on the relation between switching and intrinsic time-scales

Abstract

We have studied the dynamics of the paradigmatic Kuramoto-Sakaguchi model of identical coupled phase oscilla- tors with various kinds of time-dependent connectivity using Eulerian discretization. We first explore the parameter spaces for various types of collective states using the phase plots of the two statistical quantities, namely the strength of incoherence and the discontinity measure. In the quasi-static limit of the changing of coupling range, we have observed how the system relaxes from one state to another and have identified a few interesting collective dynamical states along the way. Under a sinusoidal change of the coupling range, the global order parameter characterizing the degree of synchronization in the system is shown to undergo a hysteresis with the coupling range. Finally, we study the low-dimensional spatio-temporal dynamics of the local order parameter in the continuum limit using the recently-developed Ott-Antonsen ansatz and justify some of our numerical results. In particular, we identify an intrinsic time-scale of the Kuramoto system and show that the simulations exhibit two distinct kinds of qualitative behavior in two cases when the time-scale associated with the switching of the coupling radius is very large compared to the intrinsic time-scale and when it is comparable with the intrinsic time-scale.