Aging transition in systems of oscillators with global distributed-delay coupling

TL;DR

This paper investigates how distributed delays in coupling affect the suppression of oscillations in networks of active and inactive oscillators, revealing conditions for aging transition based on delay distribution and coupling parameters.

Contribution

It derives new conditions for aging transition in oscillator networks with distributed-delay coupling, considering uniform and gamma delay distributions.

Findings

Increasing delay distribution width lowers the coupling threshold for aging transition.

Large mean delays in gamma distribution enable aging transition regardless of inactive oscillator proportion.

Aging transition depends on the interplay between delay distribution, coupling strength, and inactive oscillator ratio.

Abstract

We consider a globally coupled network of active (oscillatory) and inactive (non-oscillatory) oscillators with distributed-delay coupling. Conditions for aging transition, associated with suppression of oscillations, are derived for uniform and gamma delay distributions in terms of coupling parameters and the proportion of inactive oscillators. The results suggest that for the uniform distribution increasing the width of distribution for the same mean delay allows aging transition to happen for a smaller coupling strength and a smaller proportion of inactive elements. For gamma distribution with sufficiently large mean time delay, it may be possible to achieve aging transition for an arbitrary proportion of inactive oscillators, as long as the coupling strength lies in a certain range.