Global delay induced transition in a bistable system with multiplicative and additive noises

Abstract

Global time delay is introduced to a bistable system driven by multiplicative and additive noises. Approximation of small delay and numerical simulations are employed to investigate the delay induced transition. The stationary probability distribution function P st ðxÞ and the first order moment hxi st are derived. Results indicate that with the increase of global time delay, P st ðxÞ undergoes a transition from a bimodal structure to a unimodal shape and hxi st as a function of the multiplicative noise intensity exhibits suppression-like and resonance-like behavior. For the case of multiplicative noise with delay, P st ðxÞ undergoes a transition from a monostable to a bistable system. These results illustrate that global delay can control the transition of a bistable system effectively.

Force-linearization closure for non-Markovian Langevin systems with time delay

“…with a barrier of height ∆V (set to ∆V = 8 k B T ) at x/σ = 0 and two minima at x i 0 = iσ with i ∈ I = {−1, 1}. A Brownian particle in a double-well potential is a generic model for a bistable noisy system [43,44], which in recent years has been considered also under the impact of a linear delay force [17,[46][47][48][49]. As opposed to the corresponding expression given in Eq.…”

“…Bistable noisy systems often serve to study escape problems [41][42][43][44]. Bistable systems with delay have been studied theoretically, e.g., regarding the Kramers rate [17,30,45] and in the context of coherence resonance (see the study of Tsimring and Pikovsky [46], who provided a solution based on a discretization procedure, and subsequent work [17,[46][47][48]). Experimental realizations have been suggested in Refs.…”