Master Stability Functions for Coupled Near-Identical Dynamical Systems

TL;DR

This paper develops a generalized master stability function for analyzing synchronization stability in networks of nearly identical coupled dynamical systems, accounting for small parameter differences.

Contribution

It introduces a new MSF framework for near-identical systems and provides conditions for stable near-synchronization considering parameter variations.

Findings

Synchronization error scales linearly with parameter variations

Laplacian eigenvectors are crucial in near-synchronization analysis

A sufficient condition for stable near-synchronization is derived

Abstract

We derive a master stability function (MSF) for synchronization in networks of coupled dynamical systems with small but arbitrary parametric variations. Analogous to the MSF for identical systems, our generalized MSF simultaneously solves the linear stability problem for near-synchronous states (NSS) for all possible connectivity structures. We also derive a general sufficient condition for stable near-synchronization and show that the synchronization error scales linearly with the magnitude of parameter variations.Our analysis underlines significant roles played by the Laplacian eigenvectors in the study of network synchronization of near-identical systems.