The multiple effects of gradient coupling on network synchronization

TL;DR

This paper investigates how gradient coupling influences network synchronization, revealing an optimal gradient for maximum synchronizability and showing that too large a gradient can impair synchronization, especially in dense heterogeneous networks.

Contribution

It identifies the existence of an optimal coupling gradient for network synchronization and compares effects in different network types, supported by eigenvalue and oscillator simulations.

Findings

Optimal coupling gradient maximizes synchronizability

Large gradients can suppress synchronization due to network breaking

Dense heterogeneous networks better tolerate large gradients

Abstract

Recent studies have shown that synchronizability of complex networks can be significantly improved by asymmetric couplings, and increase of coupling gradient is always in favor of network synchronization. Here we argue and demonstrate that, for typical complex networks, there usually exists an optimal coupling gradient under which the maximum network synchronizability is achieved. After this optimal value, increase of coupling gradient could deteriorate synchronization. We attribute the suppression of network synchronization at large gradient to the phenomenon of network breaking, and find that, in comparing with sparsely connected homogeneous networks, densely connected heterogeneous networks have the superiority of adopting large gradient. The findings are supported by indirect simulations of eigenvalue analysis and direct simulations of coupled nonidentical oscillator networks.