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A study on stochastic resonance of one-dimensional bistable system in the neighborhood of bifurcation point with the moment method

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  • Zhang, Guang-Jun
  • Xu, Jian-Xue

Abstract

This paper analyzes the stochastic resonance induced by a novel transition of one-dimensional bistable system in the neighborhood of bifurcation point with the method of moment, which refer to the transition of system motion among a potential well of stable fixed point before bifurcation of original system and double-well potential of two coexisting stable fixed points after original system bifurcation at the presence of internal noise. The results show: the semi-analytical result of stochastic resonance of one-dimensional bistable system in the neighborhood of bifurcation point may be obtained, and the semi-analytical result is in accord with the one of Monte Carlo simulation qualitatively, the occurrence of stochastic resonance is related to the bifurcation of noisy nonlinear dynamical system moment equations, which induce the transfer of energy of ensemble average (Ex) of system response in each frequency component and make the energy of ensemble average of system response concentrate on the frequency of input signal, stochastic resonance occurs.

Suggested Citation

  • Zhang, Guang-Jun & Xu, Jian-Xue, 2006. "A study on stochastic resonance of one-dimensional bistable system in the neighborhood of bifurcation point with the moment method," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 1056-1066.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:4:p:1056-1066
    DOI: 10.1016/j.chaos.2005.04.074
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    Cited by:

    1. Kang, Yan-Mei & Jiang, Yao-Lin, 2009. "Observing bifurcation and resonance in a mean-field coupled periodically driven noisy overdamped oscillators by the method of moments," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1987-1993.
    2. Zhang, Guang-Jun & Xu, Jian-Xue & wang, Jue & Yue, Zhi-Feng & Zou, Hai-Lin, 2009. "Stochastic resonance induced by the novel random transitions of two-dimensional weak damping bistable duffing oscillator and bifurcation of moment equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2272-2279.

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