Complete Synchronization of Coupled Oscillators Based on the Contraction Theory

TL;DR

This paper uses contraction theory to analyze conditions for achieving complete synchronization in various coupled oscillator networks, including Duffing and Rayleigh van der Pol oscillators, across different topologies.

Contribution

It introduces a novel application of contraction theory combined with trapping region methods to determine synchronization conditions in complex oscillator networks.

Findings

Derived synchronization conditions for Duffing van der Pol oscillators.

Identified initial condition-dependent synchronization criteria for Rayleigh van der Pol oscillators.

Analyzed synchronization in all-to-all, star, and ring network topologies.

Abstract

This paper studies contraction theory with the aim of exploring complete synchronization phenomenon in complex networks of coupled oscillators. We examine the conditions for complete synchronization in three network topologies: all-to-all, star, and ring. Specifically, we derive the conditions under which networks of linearly coupled (Duffing) van der Pol oscillators achieve complete synchronization. Additionally, by combining contraction theory with the trapping region method, we identify the conditions for complete synchronization of networks of linearly coupled Rayleigh van der Pol oscillators under specific initial conditions.