Phase Response Curves of Coupled Oscillators

TL;DR

This paper analytically and numerically investigates how coupling influences the phase response curves of oscillators, providing formulas for weakly coupled pairs and discussing globally coupled systems.

Contribution

It derives analytical expressions for PRCs of coupled oscillators and explores their behavior in both weakly and globally coupled regimes.

Findings

PRCs for weakly coupled oscillators are analytically obtained

Coupling affects the shape and properties of PRCs

Simulation confirms analytical results

Abstract

Many real oscillators are coupled to other oscillators and the coupling can affect the response of the oscillators to stimuli. We investigate phase response curves (PRCs) of coupled oscillators. The PRCs for two weakly coupled phase-locked oscillators are analytically obtained in terms of the PRC for uncoupled oscillators and the coupling function of the system. Through simulation and analytic methods, the PRCs for globally coupled oscillators are also discussed.