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Amplitude and phase dynamics in oscillators with distributed-delay coupling.

Y N Kyrychko¹, K B Blyuss, E Schöll

¹Department of Mathematics, University of Sussex, Falmer, Brighton BN1 9QH, UK. y.kyrychko@sussex.ac.uk

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences

|August 21, 2013

Summary

This summary is machine-generated.

This study explores how distributed delays impact coupled Stuart-Landau oscillators, finding conditions for amplitude death based on frequency and coupling parameters. It also analyzes oscillatory dynamics and identifies stable phase-locked solutions under various delay distributions.

Keywords:

amplitude death distributed-delay coupling phase dynamics

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Area of Science:

Nonlinear Dynamics
Complex Systems
Coupled Oscillator Theory

Background:

Coupled oscillators are fundamental in various scientific fields.
Understanding the impact of time delays is crucial for accurate system modeling.
Non-identical oscillators introduce complexity in collective dynamics.

Purpose of the Study:

Investigate the influence of distributed-delay coupling on Stuart-Landau oscillator systems.
Determine conditions for achieving amplitude death in non-identical coupled oscillators.
Analyze oscillatory dynamics and phase-locked solutions under different delay distributions.

Main Methods:

Derivation of conditions for amplitude death using system parameters and delay characteristics.
Numerical computation of eigenvalues for stability analysis within amplitude death regions.
Employing amplitude-phase representation to study oscillatory dynamics.

Main Results:

Established conditions for amplitude death considering frequency, detuning, coupling parameters, and delay distribution properties (mean and width).
Identified various branches of phase-locked solutions.
Analyzed the stability of these solutions for uniform and gamma delay distributions.

Conclusions:

Distributed delays significantly influence the dynamics of coupled non-identical Stuart-Landau oscillators.
Amplitude death is achievable and predictable based on system and delay parameters.
The study provides insights into complex oscillatory behaviors and stable states in delayed systems.