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 \(P_{st}(x)\) and the first order moment \(\langle x\rangle _{st}\) are derived. Results indicate that with the increase of global time delay, \(P_{st}(x)\) undergoes a transition from a bimodal structure to a unimodal shape and \(\langle x\rangle _{st}\) as a function of the multiplicative noise intensity exhibits suppression-like and resonance-like behavior. For the case of multiplicative noise with delay, \(P_{st}(x)\) 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.
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