Persistence of Network Synchronization under Nonidentical Coupling Functions

TL;DR

This paper studies how network synchronization persists despite nonidentical coupling functions, revealing that network structure influences the tolerance to coupling mismatches, with Erdős-Rényi graphs allowing larger perturbations than scale-free graphs.

Contribution

It demonstrates the impact of network topology on the robustness of synchronization under nonidentical coupling functions, highlighting differences between Erdős-Rényi and scale-free networks.

Findings

Erdős-Rényi graphs support large coupling perturbations.

Scale-free graphs restrict coupling function differences as network size grows.

Network structure determines synchronization robustness under mismatched couplings.

Abstract

We investigate the persistence of synchronization in networks of diffusively coupled oscillators when the coupling functions are nonidentical. Under mild conditions, we uncover the influence of the network interaction structure on the mismatches of the coupling function. We show that Erd\"os-R\'enyi random graphs support large perturbations in the coupling function. In contrast scale-free graphs do not allow large perturbations in the coupling function, that is, as the network size n goes to infinity it forces the coupling functions to be identical.