Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 619708, 18 pages
Research Article

Adaptive Hybrid Function Projective Synchronization of Chaotic Systems with Time-Varying Parameters

School of Mathematics and Computer Science, Shanxi Normal University, Shanxi, Linfen 041004, China

Received 11 November 2011; Accepted 7 February 2012

Academic Editor: Teh-Lu Liao

Copyright © 2012 Jinsheng Xing. 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.


The adaptive hybrid function projective synchronization (AHFPS) of different chaotic systems with unknown time-varying parameters is investigated. Based on the Lyapunov stability theory and adaptive bounding technique, the robust adaptive control law and the parameters update law are derived to make the states of two different chaotic systems asymptotically synchronized. In the control strategy, the parameters need not be known throughly if the time-varying parameters are bounded by the product of a known function of t and an unknown constant. In order to avoid the switching in the control signal, a modified robust adaptive synchronization approach with the leakage-like adaptation law is also proposed to guarantee the ultimately uni-formly boundedness (UUB) of synchronization errors. The schemes are successfully applied to the hybrid function projective synchronization between the Chen system and the Lorenz system and between hyperchaotic Chen system and generalized Lorenz system. Moreover, numerical simulation results are presented to verify the effectiveness of the proposed scheme.