Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 962680, 14 pages
Research Article

Synchronization of the Extended Bonhoffer-Van der Pol Oscillators

Department of Electrical Engineering, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait

Received 19 February 2012; Revised 4 May 2012; Accepted 8 May 2012

Academic Editor: Jun-Juh Yan

Copyright © 2012 Mohamed Zribi and Saleh Alshamali. 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.


This paper deals with the synchronization of two extended Bonhoffer-Van der Pol (B-VDP) oscillators. A Lyapunov-based controller and a sliding mode controller are proposed for the synchronization of the oscillators. Both design schemes use a single input controller acting on one state only. Asymptotic stability results for the closed-loop system are derived using Lyapunov theory. It is shown that the proposed controllers effectively synchronize the driver and the response systems for the case when nominal values of the system parameters are used, and for the case when parameter perturbations are introduced. Simulation results are presented to show the effectiveness of the proposed controllers.