Resumption of dynamism in damaged networks of coupled oscillators

TL;DR

This paper introduces an external feedback scheme to revive dynamism in damaged networks of oscillators, improving survivability even with time delays and complex topologies, validated through numerical and analytical methods.

Contribution

It presents a novel feedback-based method to restore activity in damaged oscillator networks, applicable to various topologies and oscillator types, including delayed and chaotic systems.

Findings

Effective revival of oscillators in damaged networks.

Enhanced network persistence in complex topologies.

Applicability to different oscillator models, including chaotic systems.

Abstract

Deterioration in the dynamical activities may come up naturally or due to environmental influences in a massive portion of biological and physical systems. Such dynamical degradation may have outright effect on the substantive network performance. This enforces to provide some proper prescriptions to overcome undesired circumstances. Through this article, we present a scheme based on external feedback that can efficiently revive dynamism in damaged networks of active and inactive oscillators and thus enhance the network survivability. Both numerical and analytical investigations are performed in order to verify our claim. We also provide a comparative study on the effectiveness of this mechanism for feedbacks to the inactive group or to the active group only. Most importantly, resurrection of dynamical activity is realized even in time-delayed damaged networks, which are considered to be less persistent against deterioration in form of inactivity in the oscillators. Furthermore, prominence in our approach is substantiated by providing evidence of enhanced network persistence in complex network topologies taking small-world and scale-free architectures, which makes the proposed remedy quite general. Besides the study in network of Stuart-Landau oscillators, affirmative influence of external feedback has been justified in network of chaotic Rossler systems as well.