The development of generalized synchronization on complex networks

TL;DR

This paper explores how generalized synchronization develops in various complex network structures, revealing the conditions and pathways for synchronization among both identical and nonidentical chaotic oscillators, influenced by network topology and coupling strategies.

Contribution

It demonstrates that generalized synchronization can occur in diverse complex networks regardless of degree distribution and oscillator similarity, and analyzes the effects of network topology and coupling strategies.

Findings

GS occurs in heterogeneous and homogeneous networks with both identical and nonidentical oscillators.

A bifurcation path from non-synchronization to complete synchronization via GS is identified.

Network topology and coupling strategies significantly influence the development of GS.

Abstract

In this paper, we investigate the development of generalized synchronization (GS) on typical complex networks, such as scale-free networks, small-world networks, random networks and modular networks. By adopting the auxiliary-system approach to networks, we show that GS can take place in oscillator networks with both heterogeneous and homogeneous degree distribution, regardless of whether the coupled chaotic oscillators are identical or nonidentical. For coupled identical oscillators on networks, we find that there exists a general bifurcation path from initial non-synchronization to final global complete synchronization (CS) via GS as the coupling strength is increased. For coupled nonidentical oscillators on networks, we further reveal how network topology competes with the local dynamics to dominate the development of GS on networks. Especially, we analyze how different coupling strategies affect the development of GS on complex networks. Our findings provide a further understanding for the occurrence and development of collective behavior in complex networks.