Restoration of oscillation in network of oscillators in presence of direct and indirect interactions

TL;DR

This paper demonstrates that introducing a feedback factor in the coupling scheme can effectively restore oscillations in networks of oscillators suppressed by environmental and direct interactions, verified across different oscillator models.

Contribution

It proposes a novel feedback modification to coupling schemes that restores oscillations in networks affected by environmental and direct suppression mechanisms.

Findings

Feedback factor successfully restores oscillations in limit cycle and chaotic oscillators.

Restoration is effective despite parameter mismatches among oscillators.

The method applies to various types of oscillator systems.

Abstract

The suppression of oscillations in coupled systems may lead to several unwanted situations, which requires a suitable treatment to overcome the suppression. In this paper, we show that the environmental coupling in the presence of direct interaction, which can suppress oscillation even in a network of identical oscillators, can be modified by introducing a feedback factor in the coupling scheme in order to restore the oscillation. We inspect how the introduction of the feedback factor helps to resurrect oscillation from various kind of death states. We numerically verify the resurrection of oscillations for two paradigmatic limit cycle systems, namely Landau-Stuart and Van der Pol oscillators and also in generic chaotic Lorenz oscillator. We also study the effect of parameter mismatch in the process of restoring oscillation for coupled oscillators.