Resurgence of oscillation in coupled oscillators under delayed cyclic interaction

TL;DR

This paper explores how delayed cyclic interactions can cause oscillation suppression and revival in coupled oscillators, with analytical and numerical evidence showing the effects of asymmetry and feedback parameters.

Contribution

It introduces a novel mechanism for oscillation revival from amplitude death states using asymmetry and feedback in delayed cyclic coupling, supported by analytical and numerical results.

Findings

Amplitude death regions shrink with increased asymmetry and decreased feedback.

Oscillations can revive from death states in coupled limit cycle oscillators.

The mechanism applies to networks of identical oscillators and chaotic Lorenz systems.

Abstract

This paper investigates the emergence of amplitude death and revival of oscillations from the suppression states in a system of coupled dynamical units interacting through delayed cyclic mode. In order to resurrect the oscillation from amplitude death state, we introduce asymmetry and feedback parameter in the cyclic coupling forms as a result of which the death region shrinks due to higher asymmetry and lower feedback parameter values for coupled oscillatory systems. Some analytical conditions are derived for amplitude death and revival of oscillations in two coupled limit cycle oscillators and corresponding numerical simulations confirm the obtained theoretical results. We also report that the death state and revival of oscillations from quenched state are possible in the network of identical coupled oscillators. The proposed mechanism has also been examined using chaotic Lorenz oscillator.