Stochastic switching in delay-coupled oscillators

TL;DR

This paper analyzes how noise influences the switching behavior between multiple stable oscillation patterns in delay-coupled oscillators, providing analytical insights into frequency distributions and residence times.

Contribution

It introduces a reduction of delay-coupled oscillator systems to a non-delayed Langevin equation, enabling analytical computation of frequency distributions and residence times.

Findings

Number of stable orbits scales with delay and coupling strength.

System visits only a fraction of possible orbits, scaling with square root of delay.

Residence times are mainly influenced by coupling strength and number of oscillators.

Abstract

A delay is known to induce multistability in periodic systems. Under influence of noise, coupled oscillators can switch between coexistent orbits with different frequencies and different oscillation patterns. For coupled phase oscillators we reduce the delay system to a non-delayed Langevin equation, which allows us to analytically compute the distribution of frequencies, and their corresponding residence times. The number of stable periodic orbits scales with the roundtrip delay time and coupling strength, but the noisy system visits only a fraction of the orbits, which scales with the square root of the delay time and is independent of the coupling strength. In contrast, the residence time in the different orbits is mainly determined by the coupling strength and the number of oscillators, and only weakly dependent on the coupling delay. Finally we investigate the effect of a detuning between the oscillators. We demonstrate the generality of our results with delay-coupled FitzHugh-Nagumo oscillators.