On the various kinds of synchronization in delayed Duffing-Van der Pol system

A detailed investigation is performed about the various zones of stability for delayed Duffing-Van der Pol system, which in term shows the specific role of delay in the formation of the attractor. Coupling of two such similar systems gives rise to rich dynamics if the coupling also belongs to a delayed class. This gives rise to varieties of synchronization channels – such as anticipatory synchronization and retarded synchronization. As the coefficient of delayed term changes value, it is observed that anticipatory synchronization makes way to phase synchronization. The onset of these various mechanisms are tested by the computation of similarity function and probability of recurrence. In the study of phase synchronization the machinery of empirical mode decomposition (EMD) analysis is adapted and lastly maximal Lyapunov exponent is computed as a verifying criterion.