Phase resetting of collective rhythm in ensembles of oscillators

TL;DR

This paper develops an analytical framework for understanding how ensembles of coupled oscillators respond to perturbations, combining theory and numerical evidence to distinguish immediate and dynamical phase resets.

Contribution

It introduces a novel analytical approach to derive phase resetting equations for globally coupled Sakaguchi-Kuramoto oscillators using Ott-Antonsen theory.

Findings

Final phase reset comprises immediate and dynamical components.

Analytical and numerical methods agree well with simulations.

Theory applicable to large ensembles approaching the thermodynamic limit.

Abstract

Phase resetting curves characterize the way a system with a collective periodic behavior responds to perturbations. We consider globally coupled ensembles of Sakaguchi-Kuramoto oscillators, and use the Ott-Antonsen theory of ensemble evolution to derive the analytical phase resetting equations. We show the final phase reset value to be composed of two parts: an immediate phase reset directly caused by the perturbation, and the dynamical phase reset resulting from the relaxation of the perturbed system back to its dynamical equilibrium. Analytical, semi-analytical and numerical approximations of the final phase resetting curve are constructed. We support our findings with extensive numerical evidence involving identical and non-identical oscillators. The validity of our theory is discussed in the context of large ensembles approximating the thermodynamic limit.