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Stochastic resonance induced by the novel random transitions of two-dimensional weak damping bistable duffing oscillator and bifurcation of moment equation

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  • Zhang, Guang-Jun
  • Xu, Jian-Xue
  • wang, Jue
  • Yue, Zhi-Feng
  • Zou, Hai-Lin

Abstract

In this paper stochastic resonance induced by the novel random transitions of two-dimensional weak damping bistable Duffing oscillator is analyzed by moment method. This kind of novel transition refers to the one among three potential well on two sides of bifurcation point of original system at the presence of internal noise. Several conclusions are drawn. First, the semi-analytical result of stochastic resonance induced by the novel random transitions of two-dimensional weak damping bistable Duffing oscillator can be obtained, and the semi-analytical result is qualitatively compatible with the one of Monte Carlo simulation. Second, a bifurcation of double-branch fixed point curves occurs in the moment equations with noise intensity as their bifurcation parameter. Third, the bifurcation of moment equations corresponds to stochastic resonance of original system. Finally, the mechanism of stochastic resonance is presented from another viewpoint through analyzing the energy transfer induced by the bifurcation of moment equation.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:4:p:2272-2279
    DOI: 10.1016/j.chaos.2009.03.155
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    References listed on IDEAS

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    1. 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.
    2. Zhang, Guang-Jun & Xu, Jian-Xue, 2005. "Stochastic resonance induced by novel random transitions of motion of FitzHugh–Nagumo neuron model," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1439-1449.
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