A Novel Hybrid Function Projective Synchronization between Different Fractional-Order Chaotic Systems

Ping Zhou,Xiao-You Yang

doi:10.1155/2011/496846

Abstract

An adaptive hybrid function projective synchronization (AHFPS) scheme between different fractional-order chaotic systems with uncertain system parameter is addressed in this paper. In this proposed scheme, the drive and response system could be synchronized up to a vector function factor. This proposed scheme is different with the function projective synchronization (FPS) scheme, in which the drive and response system could be synchronized up to a scaling function factor. The adaptive controller and the parameter update law are gained. Two examples are presented to demonstrate the effectiveness of the proposed scheme.

Highlights

In nonlinear science, chaos synchronization is a hot topic, which has attracted much attention from scientists and engineers in the last few years 1–13
Motivated by the above discussion, an adaptive hybrid function projective synchronization AHFPS scheme between different fractional-order chaotic systems with uncertain system parameters is investigated in this paper
The drive and response system could be synchronized up to a vector function factor in this proposed scheme. This technique is applied to achieve the AHFPS between different fractional-order Lorenz systems with one uncertain system parameter, and the AHFPS between the fractionalorder Lorenz system with one uncertain system parameter and the fractional-order Chen system

Summary

Introduction

Chaos synchronization is a hot topic, which has attracted much attention from scientists and engineers in the last few years 1–13. Motivated by the above discussion, an adaptive hybrid function projective synchronization AHFPS scheme between different fractional-order chaotic systems with uncertain system parameters is investigated in this paper. The drive and response system could be synchronized up to a vector function factor in this proposed scheme. This technique is applied to achieve the AHFPS between different fractional-order Lorenz systems with one uncertain system parameter, and the AHFPS between the fractionalorder Lorenz system with one uncertain system parameter and the fractional-order Chen system.

The Fractional Derivatives and AHFPS Scheme

Applications

Conclusion