Simulation study of the effects of time delay on the correlation function of a bistable system with correlated noises

Abstract

The effects of time delay on the fluctuation properties of a bistable system are investigated by simulating its normalised correlation function C(s). Three cases including linear delay, cubic delay and global delay in the system are considered respectively. The simulation results indicate that the linear delay enhances the fluctuation of the system (reduces the stability of the system) while the cubic delay and global delay weaken it (enforce the stability of the system), and the effect of cubic delay is more pronounced than the linear delay and global delay.

Effects of linear and nonlinear time-delayed feedback on the noise-enhanced stability phenomenon in a periodically driven bistable system

“…global delayed feedback), on the rate processes of a stochastic bistable system has also been investigated by a small delay expansion [36]. More recently, the effects of linear delay, cubic delay and global delay on the fluctuation properties of a bistable system have been studied by the stochastic simulation method [37]. In our previous studies, we investigated the effect of time delay on the NES effect in a metastable system, and it was found that the increase of the delay time can enhance or weaken the NES effect [38]- [40].…”