Sync: Persistence in Two Diffusively Coupled Oscillators

TL;DR

This paper investigates the stability of synchronization in two diffusively coupled oscillators under small perturbations, analyzing both linear and nonlinear cases using Lyapunov and Hartman-Grobman methods.

Contribution

It introduces a comprehensive stability analysis framework for coupled oscillators considering both linear and nonlinear perturbations.

Findings

Global stability guaranteed for linear perturbations using Lyapunov method

Local stability analysis for nonlinear perturbations via Hartman-Grobman theorem

Provides theoretical conditions for synchronization stability in coupled oscillators

Abstract

We address the problem of stability of synchronization in two diffu- sively coupled oscillators under small perturations. We have two cases, namely, when the perturation becomes of a linear operator and the case of non-linear operator. We use the Lyapunov second method to guar- antee the global analysis for the first case. For the second, we use the Hartman-Grobman theorem, providing local analysis.