Synchronizing modified van der Pol–Duffing oscillators with offset terms using observer design: application to secure communications

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This study addresses the adaptive synchronization of the modified van der Pol–Duffing (MVDPD) oscillator with offset terms. From our investigations of the system dynamics, we obtain that the system presents a chaotic behaviour at weak values of the offset parameters. Routh–Hurwitz criteria are used to study the asymptotic stability of the steady states. An adaptive observer design method is applied to achieve synchronization of two identical MVDPD oscillators with offset. Numerical simulations are given to validate the proposed synchronization approach. Moreover, as an application, the proposed scheme is applied to secure communication. Also, simulation results verify the proposed scheme's success in the communication application.