Synchronization of coupled nonidentical dynamical systems

TL;DR

This paper develops an approximate Master Stability Function to analyze and optimize the synchronization stability of coupled nearly identical dynamical systems on networks, revealing design principles for improved synchronizability.

Contribution

It introduces an approximate MSF for nearly identical systems and identifies network design strategies to enhance synchronization stability.

Findings

Edges connecting nodes with larger parameter mismatch improve synchronizability.

Nodes at parameter mismatch extremes are preferred as hubs.

The method guides network design for better synchronization.

Abstract

We analyze the stability of synchronized state for coupled nearly identical dynamical systems on networks by deriving an approximate Master Stability Function (MSF). Using this MSF we treat the problem of designing a network having the best synchronizability properties. We find that the edges which connect nodes with a larger relative parameter mismatch are preferred and the nodes having values at one extreme of the parameter mismatch are preferred as hubs.