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Synchronization of the Extended Bonhoffer-Van der Pol Oscillators

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  • Mohamed Zribi
  • Saleh Alshamali

Abstract

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.

Suggested Citation

  • Mohamed Zribi & Saleh Alshamali, 2012. "Synchronization of the Extended Bonhoffer-Van der Pol Oscillators," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-14, June.
    • Handle: RePEc:hin:jnlmpe:962680
    DOI: 10.1155/2012/962680
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