Synchronization Stability of Coupled Near-Identical Oscillator Network

TL;DR

This paper develops a general framework using master stability functions to analyze how parameter mismatches affect synchronization stability in networks of near-identical oscillators, demonstrated on Lorenz systems and scale-free networks.

Contribution

It introduces master stability equations for near-identical oscillators, enabling structure-independent analysis of synchronization stability under parameter mismatch.

Findings

Network architecture influences synchronization stability similarly despite mismatch patterns.

Master stability functions effectively analyze near-identical oscillator networks.

Synchronization stability is robust across different network types with parameter mismatches.

Abstract

We derive variational equations to analyze the stability of synchronization for coupled near-identical oscillators. To study the effect of parameter mismatch on the stability in a general fashion, we define master stability equations and associated master stability functions, which are independent of the network structure. In particular, we present several examples of coupled near-identical Lorenz systems configured in small networks (a ring graph and sequence networks) with a fixed parameter mismatch and a large Barabasi-Albert scale-free network with random parameter mismatch. We find that several different network architectures permit similar results despite various mismatch patterns.