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

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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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Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 11247027), the West Light Foundation of The Chinese Academy of Sciences and and the Science Foundation of Yunnan University.

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Authors and Affiliations

  1. Department of Physics, Yunnan University, Kunming, 650091, China

    L. C. Du & D. C. Mei

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  1. L. C. Du
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  2. D. C. Mei
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Correspondence to L. C. Du.

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Du, L.C., Mei, D.C. Global delay induced transition in a bistable system with multiplicative and additive noises. Indian J Phys 89, 267–272 (2015). https://doi.org/10.1007/s12648-014-0581-8

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