Aging transition under discrete time-dependent coupling: Restoring rhythmicity from aging

TL;DR

This paper investigates how discrete time-dependent coupling in oscillator networks can reduce aging effects and restore rhythmic oscillatory behavior, with implications for controlling dynamics in complex systems.

Contribution

It introduces a novel approach using discrete time-dependent coupling to effectively shrink aging regions and restore oscillations in coupled oscillator networks.

Findings

Aging region shrinks with increasing ON-OFF interval period.

Asymmetric coupling with longer OFF intervals more effectively revives oscillations.

Pulse interval critically influences aging transition and rhythmicity restoration.

Abstract

We explore the aging transition in a network of globally coupled Stuart-Landau oscillators under a discrete time-dependent coupling. In this coupling, the connections among the oscillators are turned ON and OFF in a systematic manner, having either a symmetric or an asymmetric time interval. We discover that depending upon the time period and duty cycle of the ON-OFF intervals, the aging region shrinks drastically in the parameter space, therefore promoting restoration of oscillatory dynamics from the aging. In the case of symmetric discrete coupling (where the ON-OFF intervals are equal), the aging zone decreases significantly with the resumption of dynamism with an increasing time period of the ON-OFF intervals. On the other hand, in the case of asymmetric coupling (where the ON-OFF intervals are not equal), we find that the ratio of the ON and OFF intervals controls the aging dynamics: the aging state is revoked more effectively if the interval of the OFF state is greater than the ON state. Finally, we study the transition in aging using a discrete pulse coupling: we note that the pulse interval plays a crucial role in determining the aging region. For all the cases of discrete time-dependent couplings, the aging regions are shrinking and the rhythmicity gets enhanced in a controlled manner. Our findings suggest that this type of coupling can act as a noninvasive way to restore the oscillatory dynamics from an aging state in a network of coupled oscillators.