Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 916140, 16 pages
http://dx.doi.org/10.1155/2012/916140
Research Article

Adaptive Projective Synchronization between Two Different Fractional-Order Chaotic Systems with Fully Unknown Parameters

Liping Chen,1,2 Shanbi Wei,1 Yi Chai,1,2 and Ranchao Wu3

1School of Automation, Chongqing University, Chongqing 400044, China
2State Key Laboratory of Power Transmission Equipment and System Security and New Technology, Chongqing University, Chongqing 400044, China
3School of Mathematics, Anhui University, Hefei 230039, China

Received 13 September 2011; Revised 20 November 2011; Accepted 20 November 2011

Academic Editor: Piermarco Cannarsa

Copyright © 2012 Liping Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Projective synchronization between two different fractional-order chaotic systems with fully unknown parameters for drive and response systems is investigated. On the basis of the stability theory of fractional-order differential equations, a suitable and effective adaptive control law and a parameter update rule for unknown parameters are designed, such that projective synchronization between the fractional-order chaotic Chen system and the fractional-order chaotic Lü system with unknown parameters is achieved. Theoretical analysis and numerical simulations are presented to demonstrate the validity and feasibility of the proposed method.