Collective dynamical response of coupled oscillators with any network structure

TL;DR

This paper develops a comprehensive reduction theory for analyzing how coupled oscillator networks respond collectively to external stimuli, regardless of network structure, with applications to frequency synchronization.

Contribution

It introduces a general framework for deriving phase sensitivity and coupling in any network structure, extending analysis to nonuniform external forcing.

Findings

Derived general formulas for collective phase sensitivity.

Applicable to any network structure undergoing frequency synchronization.

Illustrated the theory with multiple example networks.

Abstract

We formulate a reduction theory that describes the response of an oscillator network as a whole to external forcing applied nonuniformly to its constituent oscillators. The phase description of multiple oscillator networks coupled weakly is also developed. General formulae for the collective phase sensitivity and the effective phase coupling between the oscillator networks are found. Our theory is applicable to a wide variety of oscillator networks undergoing frequency synchronization. Any network structure can systematically be treated. A few examples are given to illustrate our theory.