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

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.