Amplitude death in systems of coupled oscillators with distributed-delay coupling

TL;DR

This study investigates how distributed delays in coupling affect the suppression of oscillations in coupled Stuart-Landau oscillators, revealing conditions under which amplitude death occurs and how delay distribution width influences this.

Contribution

It provides analytical conditions for amplitude death with distributed delays and demonstrates how delay distribution width and phase impact oscillation suppression.

Findings

Larger delay distribution widths expand amplitude death regions.

Amplitude death can occur for any average delay with sufficient distribution width.

Coupling phase reduces the likelihood of amplitude death.

Abstract

This paper studies the effects of coupling with distributed delay on the suppression of oscillations in a system of coupled Stuart-Landau oscillators. Conditions for amplitude death are obtained in terms of strength and phase of the coupling, as well as the mean time delay and the width of the delay distribution for uniform and gamma distributions. Analytical results are confirmed by numerical computation of the eigenvalues of the corresponding characteristic equations. These results indicate that larger widths of delay distribution increase the regions of amplitude death in the parameter space. In the case of a uniformly distributed delay kernel, for sufficiently large width of the delay distribution it is possible to achieve amplitude death for an arbitrary value of the average time delay, provided that the coupling strength has a value in the appropriate range. For a gamma distribution of delay, amplitude death is also possible for an arbitrary value of the average time delay, provided that it exceeds a certain value as determined by the coupling phase and the power law of the distribution. The coupling phase has a destabilizing effect and reduces the regions of amplitude death.