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Bifurcations of forced oscillators with fuzzy uncertainties by the generalized cell mapping method

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  • Hong, Ling
  • Sun, Jian-Qiao

Abstract

In this paper, bifurcations in dynamical systems with fuzzy uncertainties are studied by means of the fuzzy generalized cell mapping (FGCM) method. A bifurcation parameter is modeled as a fuzzy set with a triangular membership function. We first study a boundary crisis resulting from a collision of a fuzzy chaotic attractor with a fuzzy saddle on the basin boundary. The fuzzy chaotic attractor together with its basin of attraction is eradicated as the fuzzy control parameter reaches a critical point. We also show that a saddle-node bifurcation is caused by the collision of a fuzzy period-one attractor with a fuzzy saddle on the basin boundary. The fuzzy attractor together with its basin of attraction suddenly disappears as the fuzzy parameter passes through a critical value.

Suggested Citation

  • Hong, Ling & Sun, Jian-Qiao, 2006. "Bifurcations of forced oscillators with fuzzy uncertainties by the generalized cell mapping method," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 895-904.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:4:p:895-904
    DOI: 10.1016/j.chaos.2005.04.118
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    References listed on IDEAS

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    1. He, Qun & Xu, Wei & Rong, Haiwu & Fang, Tong, 2004. "Stochastic bifurcation in Duffing–Van der Pol oscillators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(3), pages 319-334.
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    Cited by:

    1. Han, Qun & Xu, Wei & Sun, Jian-Qiao, 2016. "Stochastic response and bifurcation of periodically driven nonlinear oscillators by the generalized cell mapping method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 115-125.
    2. Han, Qun & Xu, Wei & Yue, Xiaole, 2016. "Exit location distribution in the stochastic exit problem by the generalized cell mapping method," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 302-306.

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    1. Han, Qun & Xu, Wei & Sun, Jian-Qiao, 2016. "Stochastic response and bifurcation of periodically driven nonlinear oscillators by the generalized cell mapping method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 115-125.

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