Stochastic resonance in a time-delayed asymmetric bistable system with mixed periodic signal

doi:10.1088/1674-1056/19/4/040503

中国物理B ›› 2010, Vol. 19 ›› Issue (4): 40503-040503.doi: 10.1088/1674-1056/19/4/040503

Stochastic resonance in a time-delayed asymmetric bistable system with mixed periodic signal

郭永峰, 徐伟, 王亮

Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China

收稿日期:2009-06-20 修回日期:2009-07-07 出版日期:2010-04-15 发布日期:2010-04-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos.~10872165 and 10902085).

Stochastic resonance in a time-delayed asymmetric bistable system with mixed periodic signal

Guo Yong-Feng(郭永峰)^†,Xu Wei(徐伟), and Wang Liang(王亮)

Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China

Received:2009-06-20 Revised:2009-07-07 Online:2010-04-15 Published:2010-04-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos.~10872165 and 10902085).

摘要/Abstract

摘要： This paper studies the phenomenon of stochastic resonance in an asymmetric bistable system with time-delayed feedback and mixed periodic signal by using the theory of signal-to-noise ratio in the adiabatic limit. A general approximate Fokker--Planck equation and the expression of the signal-to-noise ratio are derived through the small time delay approximation at both fundamental harmonics and mixed harmonics. The effects of the additive noise intensity $Q$, multiplicative noise intensity $D$, static asymmetry $r$ and delay time $\tau$ on the signal-to-noise ratio are discussed. It is found that the higher mixed harmonics and the static asymmetry $r$ can restrain stochastic resonance, and the delay time $\tau $ can enhance stochastic resonance. Moreover, the longer the delay time $\tau $ is, the larger the additive noise intensity $Q$ and the multiplicative noise intensity $D$ are, when the stochastic resonance appears.

Abstract: This paper studies the phenomenon of stochastic resonance in an asymmetric bistable system with time-delayed feedback and mixed periodic signal by using the theory of signal-to-noise ratio in the adiabatic limit. A general approximate Fokker--Planck equation and the expression of the signal-to-noise ratio are derived through the small time delay approximation at both fundamental harmonics and mixed harmonics. The effects of the additive noise intensity $Q$, multiplicative noise intensity $D$, static asymmetry $r$ and delay time $\tau$ on the signal-to-noise ratio are discussed. It is found that the higher mixed harmonics and the static asymmetry $r$ can restrain stochastic resonance, and the delay time $\tau $ can enhance stochastic resonance. Moreover, the longer the delay time $\tau $ is, the larger the additive noise intensity $Q$ and the multiplicative noise intensity $D$ are, when the stochastic resonance appears.

Key words: stochastic resonance, time-delayed feedback, mixed periodic signal, signal-to-noise ratio

中图分类号: (Noise)

05.40.Ca

02.50.Fz (Stochastic analysis) 05.10.Gg (Stochastic analysis methods)

郭永峰, 徐伟, 王亮. Stochastic resonance in a time-delayed asymmetric bistable system with mixed periodic signal[J]. 中国物理B, 2010, 19(4): 40503-040503.

Guo Yong-Feng(郭永峰),Xu Wei(徐伟), and Wang Liang(王亮). Stochastic resonance in a time-delayed asymmetric bistable system with mixed periodic signal[J]. Chin. Phys. B, 2010, 19(4): 40503-040503.

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Stochastic resonance in a time-delayed asymmetric bistable system with mixed periodic signal

Stochastic resonance in a time-delayed asymmetric bistable system with mixed periodic signal

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