Amplitude and phase dynamics in oscillators with distributed-delay coupling

TL;DR

This study explores how distributed delay coupling influences the dynamics of non-identical Stuart-Landau oscillators, revealing conditions for amplitude death and analyzing stability of phase-locked solutions.

Contribution

It provides new conditions for amplitude death in oscillators with distributed delays and analyzes the stability of phase-locked states for different delay distributions.

Findings

Conditions for amplitude death depend on average frequency, detuning, and coupling parameters.

Eigenvalues computed numerically reveal dynamics within amplitude death regions.

Various phase-locked solutions are identified and their stability analyzed.

Abstract

This paper studies the effects of distributed delay coupling on the dynamics in a system of non-identical coupled Stuart-Landau oscillators. For uniform and gamma delay distribution kernels, conditions for amplitude death are obtained in terms of average frequency, frequency detuning and parameters of the coupling, including coupling strength and phase, as well as the mean time delay and the width of the delay distribution. To gain further insight into the dynamics inside amplitude death regions, eigenvalues of the corresponding characteristic equations are computed numerically. Oscillatory dynamics of the system is also investigated using amplitude and phase representation. Various branches of phase-locked solutions are identified, and their stability is analysed for different types of delay distributions.