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

TL;DR

This paper introduces a feedback-based mechanism to revive oscillations in systems where they have been suppressed, demonstrating its effectiveness through analytical and numerical methods, even with limited feedback.

Contribution

It presents a novel feedback approach to resurrect oscillations from amplitude death states, applicable to general systems and effective with minimal feedback.

Findings

Feedback can successfully revive oscillations from death states.

The technique is effective even with feedback from few oscillators.

Analytical and numerical evidence supports the method's general applicability.

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.