Synchronization in Networks of Diffusively Coupled Nonlinear Systems: Robustness Against Time-Delays

TL;DR

This paper investigates the robustness of synchronization in networks of nonlinear systems with time delays, identifying conditions and network design principles that ensure synchronization despite delays, supported by simulations of neural oscillators.

Contribution

It establishes the existence of a unimodal parameter region for synchronization in delayed networks and analyzes how network topology affects robustness.

Findings

Existence of a unimodal region in parameter space for synchronization.

Scaling laws for the unimodal region with network topology.

Validation through simulations of neural oscillators.

Abstract

In this manuscript, we study the problem of robust synchronization in networks of diffusively time-delayed coupled nonlinear systems. In particular, we prove that, under some mild conditions on the input-output dynamics of the systems and the network topology, there always exists a unimodal region in the parameter space (coupling strength versus time-delay), such that if they belong to this region, the systems synchronize. Moreover, we show how this unimodal region scales with the network topology, which, in turn, provides useful insights on how to design the network topology to maximize robustness against time-delays. The results are illustrated by extensive simulation experiments of time-delayed coupled Hindmarsh-Rose neural chaotic oscillators.