Dynamics in a Bistable-Element-Network with Delayed Coupling and Local Noise

TL;DR

This paper investigates how an ensemble of bistable elements with delayed coupling and local noise exhibits complex dynamics, including phase transitions, oscillatory states, and coherence resonance, using numerical and analytical methods.

Contribution

It introduces a combined numerical and analytical study of bistable-element networks with delay and noise, revealing phase transitions and coherence resonance phenomena.

Findings

System undergoes phase transition with positive feedback.

Multiple coexisting oscillatory states are observed.

Maximum oscillation amplitude occurs at an optimal noise level.

Abstract

The dynamics of an ensemble of bistable elements under the influence of noise and with global time-delayed coupling is studied numerically by using a Langevin description and analytically by using 1) a Gaussian approximation and 2) a dichotomous model. We find that for a strong enough positive feedback the system undergoes a phase transition and adopts a non-zero stationary mean field. A variety of coexisting oscillatory mean field states are found for positive and negative couplings. The magnitude of the oscillatory states is maximal for a certain noise temperature, i.e., the system demonstrates the phenomenon of coherence resonance. While away form the transition points the system dynamics is well described by the Gaussian approximation, near the bifurcations it is more adequately described by the dichotomous model.