Death Behavior of Mean-Field Coupled van der Pol Oscillators Induced by Time-Delayed Feedback

Explosive death in coupled nonlinear oscillators has been an active area of extensive research in nonlinear dynamics in the recent decades. Depending on proper choice of network topology, coupling scenarios, and feedback strength, explosive death can be revealed. In this work, for the first time, we report the effect of delayed feedback on the death behavior in an ensemble of identical mean-field coupled van der Pol oscillators. In both systems with or without time delay, the normalized amplitude exhibits an abrupt transition between the oscillatory state and the death state. Intriguingly, the presence of time delay in the coupling may induce the normalized amplitude of all oscillators in the network to experience a step-like descent with small jumps in approaching the death state, pulling back the forward and backward transition points. The backward transition point has been explicitly obtained, which is confirmed by the numerical results.