Explosive and semi-explosive transitions in parametrically perturbed systems

Abstract

The phenomenon of transition between steady states, namely amplitude death and oscillation death, is identified in certain models of coupled parametrically driven nonlinear oscillators. Intriguingly, the nature of the transition is explosive. It is significant to note that this observation of explosive transition has been made in systems of identical coupled oscillators with repulsive mean-field coupling. In particular, we find that when the coupling strength increases, there are semi-explosive transitions in parametrically perturbed duffing oscillators and explosive transitions in parametrically perturbed van der Pol oscillators. We obtain analytical expressions for the critical bifurcation points through linear stability analysis. Detailed numerical studies have been performed to confirm the phenomenon.