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This paper investigates impulsive synchronization of multilinks delayed coupled complex networks with perturb effects. Based on the comparison theory of impulsive differential system, a novel synchronization criterion is derived and an impulsive controller is designed simultaneously. Finally, numerical simulations demonstrate the effectiveness of the proposed synchronization criteria.

In the past few decades, the problem of control and synchronization of complex dynamical networks has been extensively investigated in various fields of science and engineering due to its many potential practical applications [

The rest of this work is organized as follows. Section

In [

In [

In the paper, we have the following mathematical preliminaries.

We assume that

We also assume that

In this section, we will investigate impulsive synchronization of the complex networks with perturb functions. The multidelayed coupled complex network with perturb functions can be described by

We take the network given by (

Let

Let Assumptions

We choose a nonnegative function as

Then the differentiation of

On the other hand, when

When

When

Systems (

Normally, it is difficult to control a complex networks by adding the controllers to all nodes, so it would be much better to use the pinning control method since the most complex networks have large number of nodes [

For the transportation network, we all know that the transmission speed is different among highway network, railway network and airline network. So we can use multilinks delayed to describe these networks [

It is well known that the Lorenz system families are typical chaotic systems and the Lü chaotic system is a member of the families which is known as [

It is well known that the Lü attractor is bounded. Here we suppose that all nodes are running in the given bounded region. Our numerical analyses show that there exist constants

Satisfying

According to Section

In numerical simulation, let

Synchronization errors with time

This paper deals with the problem of impulsive synchronization of multilinks delayed coupled complex networks with perturb effects. On the basis of the comparison theory of impulsive differential system, the novel synchronization criteriion is derived and an impulsive controller is designed simultaneously. Finally, numerical simulations are presented to verify the effectiveness of the proposed synchronization criteria.

The authors would like to thank the referees and the editor for their valuable comments and suggestions. This research is supported by the National Natural Science Foundation of China (61075060), the Science and Technology Research Key Program for the Education Department of Hubei Province of China (D20105001 and D20126002), the Excellent Young Key Talents Cultivation Plan of Hubei Province, China Postdoctoral Science Foundation (2012M511663), the Research Fund for the Technology Development Program of Higher School of Tianjin (20111004), the Social Science Planning Project of Tianjin (TJLJ11-009), and the young talents Fund of Anhui Provinc of China (2011SQRL164).