Feedback as a mechanism for the resurrection of oscillations from death state

Abstract

The quenching of oscillations in interacting systems leads to several unwanted situations, which necessitate a suitable remedy to overcome the quenching. In this connection, this work addresses a mechanism that can resurrect oscillations in a typical situation. Through both numerical and analytical studies, we show the candidate which is capable of resurrecting oscillations is nothing but the feedback, the one which is profoundly used in dynamical control and in bio-therapies. Even in the case of a rather general system, we demonstrate analytically the applicability of the technique over one of the oscillation quenched states called amplitude death state. We also discuss some of the features of this mechanism such as adaptability of the technique with the feedback of only a few of the oscillators.