Dynamics of an Ensemble of Noisy Bistable Elements with Global Time-Delayed Coupling

TL;DR

This paper investigates how noise influences the collective behavior of globally coupled bistable elements with time delays, revealing phenomena like ordering, multi-stability, and coherence resonance through analytical and numerical methods.

Contribution

It introduces a combined analytical and numerical analysis of noisy, time-delayed bistable ensembles, highlighting new insights into their multi-stability and resonance phenomena.

Findings

System exhibits ordering transitions depending on noise level.

Presence of multi-stability with stable oscillatory states.

Maximum coherence resonance occurs at an optimal noise level.

Abstract

The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates multi-stability. That is, for a strong enough positive feedback it exhibits a non-zero stationary mean field and a variety of stable oscillatory mean field states are accessible for positive and negative feedback. The regularity of the oscillatory states is maximal for a certain noise level, i.e., the system demonstrates coherence resonance. While away from the transition points the system dynamics is well described by a Gaussian approximation, near the bifurcation points a description in terms of a dichotomous theory is more adequate.