Enhancement of dynamical robustness in a mean-field coupled network through self-feedback delay

TL;DR

This paper introduces a delayed negative self-feedback control method that significantly enhances the dynamical robustness of mean-field coupled oscillator networks, effective across different topologies and oscillator types.

Contribution

The study presents a novel control scheme using delayed negative self-feedback to improve robustness in mean-field coupled networks, applicable to various oscillator models and topologies.

Findings

Robustness increases significantly with small delay values.

The scheme restores oscillations even when all oscillators are at equilibrium.

Effectiveness is independent of network topology and oscillator type.

Abstract

In this article, we propose a very efficient technique to enhance the dynamical robustness for a network of mean-field coupled oscillators experiencing aging transition. In particular, we present a control mechanism based on delayed negative self-feedback, which can effectively enhance dynamical activities in a mean-field coupled network of active and inactive oscillators. Even for a small value of delay, robustness gets enhanced to a significant level. In our proposed scheme, the enhancing effect is more pronounced for strong coupling. To our surprise even if all the oscillators perturbed to equilibrium mode delayed negative self-feedback able to restore oscillatory activities in the network for strong coupling strength. We demonstrate that our proposed mechanism is independent of coupling topology. For a globally coupled network, we provide numerical and analytical treatment to verify our claim. Also, for global coupling to establish the generality of our scheme, we validate our results for both Stuart-Landau limit cycle oscillators and chaotic Rossler oscillators. To show that our scheme is independent of network topology, we also provide numerical results for the local mean-field coupled complex network.