Hub-Induced Synchronization in Scale-Free Networks with Cluster Structure

Jianbao Zhang,Jinde Cao,Zhongjun Ma

doi:10.1155/2014/149453

Abstract

A recent research indicated that the corticocortical connectivity network of the cat possesses cluster structure and that each cluster in the network is scale-free and has a most connected hub. Motivated by that research, we slightly modify the network model and derive sufficient conditions for cluster synchronization of the modified network based on Lyapunov function method. The obtained results indicate that cluster synchronization can be induced by the hubs of the scale-free networks. In our opinion, the concept of hub-induced synchronization provides a better understanding of cluster synchronization in scale-free networks. Numerical examples are provided to demonstrate the effectiveness of the theoretical results.

Highlights

In order to better understand the brain functions of mammals such as memory, language, and consciousness, many researches have been carried out to explore the organization and structure of the cerebral cortex [1,2,3]
Motivated by the recent researches on synchronization in scale-free networks [9,10,11], we focus on analyzing the key role of the cluster hubs in process of cluster synchronization
In order to mimic the topology structure of the corticocortical connectivity network, this paper has proposed a network model with a scale-free feature, cluster structure, and the property that each cluster has a cluster hub

Summary

Introduction

In order to better understand the brain functions of mammals such as memory, language, and consciousness, many researches have been carried out to explore the organization and structure of the cerebral cortex [1,2,3]. The network model is shown to exhibit a cluster structure with each cluster being scale-free, neither fully regular, nor completely random [4, 5]. Each of these clusters composed by cortical areas forms an organization playing common functional roles. We aim to model the cat cortex structure through building a coupled oscillator network with a scalefree feature and to study cluster synchronization in such a network. Motivated by the recent researches on synchronization in scale-free networks [9,10,11], we focus on analyzing the key role of the cluster hubs in process of cluster synchronization.

Preliminaries

Cluster Synchronization Induced by Cluster Hubs

Numerical Simulations

Conclusion