Cooperative Dynamics in a Network of Stochastic Elements with Delayed Feedback

TL;DR

This paper investigates the complex dynamics of networks composed of noise-activated bistable elements with delayed feedback, revealing phase transitions, multi-stability, and various oscillatory behaviors through numerical and analytical methods.

Contribution

It introduces a combined numerical and analytical study of stochastic networks with delay, highlighting new phenomena like delay-dependent oscillations and stability effects.

Findings

Identification of ordering phase transitions and multi-stability.

Delay-dependent oscillatory states with frequencies tied to delay distribution.

Observation of coherence resonance, amplitude death, and chaos influenced by delay properties.

Abstract

Networks of globally coupled, noise activated, bistable elements with connection time delays are considered. The dynamics of these systems is studied numerically using a Langevin description and analytically using (1) a Gaussian approximation as well as (2) a dichotomous model. The system demonstrates ordering phase transitions and multi-stability. That is, for a strong enough feedback it exhibits nontrivial stationary states and oscillatory states whose frequencies depend only on the mean of the time delay distribution function. Other observed dynamical phenomena include coherence resonance and, in the case of non-uniform coupling strengths, amplitude death and chaos. Furthermore, an increase of the stability of the trivial equilibrium with increasing non-uniformity of the time delays is observed.