Adaptive Synchronization in Complex Network with Different Order Node Dynamics

Fan-Di Zhang,Jin-Ping Jia,Li-Xin Yang

doi:10.1155/2015/919146

Fan-Di Zhang, Jin-Ping Jia + Show 1 more

Open Access

https://doi.org/10.1155/2015/919146

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Abstract

This paper investigates the adaptive cluster synchronization in the complex networks with different orders. By means of Lyapunov stability theory and the adaptive control technique, a novel adaptive synchronization controller is developed. To demonstrate the validity of the proposed method, the examples for the synchronization of systems with the chaotic and hyperchaotic node dynamics are presented.

Highlights

In the past few years, complex networks have attracted more and more attention; examples of complex networks include the Internet, social networks, biological networks, organizational networks, neural networks, and many others [1–6].A complex network can be seen as a large set of interconnected nodes and used to describe various systems with specific contents
This paper investigates the adaptive cluster synchronization in the complex networks with different orders
We focus on cluster synchronization where the local dynamics of the nodes in each group differ

Summary

Introduction

In the past few years, complex networks have attracted more and more attention; examples of complex networks include the Internet, social networks, biological networks, organizational networks, neural networks, and many others [1–6]. Synchronization constitutes one of the most prevalent collective dynamics in complex networked systems. It should be noted that complex networks consisting of different nodes are ubiquitous in various fields. We focus on cluster synchronization where the local dynamics of the nodes in each group differ. In many technological, social, and biological networks, which can be divided naturally into several groups by certain rules, nodes in the same group often have the same type of function. Much research effort has been devoted to investigating the cluster synchronization of complex dynamical networks [15, 16]. The cluster synchronization where the local dynamics of the nodes in each group differ is a more interesting topic.

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Synchronization Scheme

Conclusions