Journal of Applied Mathematics
Volume 2012 (2012), Article ID 762807, 18 pages
http://dx.doi.org/10.1155/2012/762807
Research Article

Inverse Projective Synchronization between Two Different Hyperchaotic Systems with Fractional Order

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

1State Key Laboratory of Power Transmission Equipment & System Security and New Technology, Chongqing University, Chongqing 400030, China
2School of Automation, Chongqing University, Chongqing 400030, China
3School of Mathematics, Anhui University, Hefei 230039, China

Received 14 July 2011; Accepted 5 October 2011

Academic Editor: Yuri Sotskov

Copyright © 2012 Yi Chai 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

This paper mainly investigates a novel inverse projective synchronization between two different fractional-order hyperchaotic systems, that is, the fractional-order hyperchaotic Lorenz system and the fractional-order hyperchaotic Chen system. By using the stability theory of fractional-order differential equations and Lyapunov equations for fractional-order systems, two kinds of suitable controllers for achieving inverse projective synchronization are designed, in which the generalized synchronization, antisynchronization, and projective synchronization of fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system are also successfully achieved, respectively. Finally, simulations are presented to demonstrate the validity and feasibility of the proposed method.