Generalized Projective Synchronization between Two Different Neural Networks with Mixed Time Delays

Xuefei Wu,Xuan Zhou,Yi Zhao,Chen Xu,Jianwen Feng

doi:10.1155/2012/153542

Xuefei Wu, Xuan Zhou + Show 3 more

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https://doi.org/10.1155/2012/153542

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Abstract

The generalized projective synchronization (GPS) between two different neural networks with nonlinear coupling and mixed time delays is considered. Several kinds of nonlinear feedback controllers are designed to achieve GPS between two different such neural networks. Some results for GPS of these neural networks are proved theoretically by using the Lyapunov stability theory and the LaSalle invariance principle. Moreover, by comparison, we determine an optimal nonlinear controller from several ones and provide an adaptive update law for it. Computer simulations are provided to show the effectiveness and feasibility of the proposed methods.

Highlights

Over the past two decades, the investigation on the synchronization of complex networks has attracted a great deal of attention due to its potential applications in various fields, such as physics, mathematics, secure communication, engineering, automatic control, biology, and sociology 1–9
In 29, Feng et al investigated projectiveanticipating and projective-lag synchronization on complex dynamical networks composed of a large number of interconnected components, in which the dynamics of the nodes of the complex networks were time-delayed chaotic systems without the limitation of the partial linearity
The GPS between two neural networks with mixed time delays and different parameters was investigated in this paper

Summary

Introduction

Over the past two decades, the investigation on the synchronization of complex networks has attracted a great deal of attention due to its potential applications in various fields, such as physics, mathematics, secure communication, engineering, automatic control, biology, and sociology 1–9. Discrete Dynamics in Nature and Society the synchronized states, so it is an interesting research topic and has many applications If this proportional feature is applied to M-nary digital communication, the communication speed can be accelerated substantially. In , Chen et al studied projective synchronization of time-delayed chaotic systems in a driven-response complex network, where the nodes are not partially linear and the scale factors are different from each other. In , Feng et al investigated projectiveanticipating and projective-lag synchronization on complex dynamical networks composed of a large number of interconnected components, in which the dynamics of the nodes of the complex networks were time-delayed chaotic systems without the limitation of the partial linearity. In 31 , Zheng et al probed into adaptive projective synchronization between two complex networks with different topological structures, its systems contained time-varying delays.

Model Description and Preliminaries

GPS between Two Different Neural Networks with Mixed Time Delays

Numerical Simulations

Conclusion