Strange attractors and synchronization dynamics of coupled Van der Pol–Duffing oscillators

We consider in this paper the synchronization dynamics of coupled chaotic Van der Pol–Duffing systems. We first find that with the judicious choose of the set of initial conditions, the model exhibits two strange chaotic attractors. The problem of synchronizing chaos both on the same and different chaotic orbits of two coupled Van der Pol–Duffing systems is investigated. The stability boundaries of the synchronization process between two coupled driven Van der Pol model are derived and the effects of the amplitude of the periodic perturbation of the coupling parameter on these boundaries are analyzed. The results are provided on the stability map in the (q, K) plane.