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Effect of bounded noise on chaotic motions of stochastically perturbed slowly varying oscillator

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  • Chen, Zhen
  • Liu, X.B.

Abstract

The effect of bounded noise on the chaotic behavior of a class of slowly varying oscillators is investigated. The stochastic Melnikov method is employed and then the criteria in both mean and mean-square sense are derived. The threshold amplitude of bounded noise given by stochastic Melnikov process is in good comparison with one determined by the numerical simulation of top Lyapunov exponents. The presence of noise scatters the chaotic domain in parameter space and the larger noise intensity results in a sparser and more irregular region. Both the simple cell mapping method and the generalized cell mapping method are applied to demonstrate the effects of noises on the attractors. Results show that the attractors are diffused and smeared by bounded noise and if the noise intensity increases, the diffusion is exacerbated.

Suggested Citation

  • Chen, Zhen & Liu, X.B., 2015. "Effect of bounded noise on chaotic motions of stochastically perturbed slowly varying oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 72-81.
    • Handle: RePEc:eee:chsofr:v:76:y:2015:i:c:p:72-81
    DOI: 10.1016/j.chaos.2015.02.024
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    References listed on IDEAS

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    1. Yang, Xiaoli & Xu, Wei & Sun, Zhongkui & Fang, Tong, 2005. "Effect of bounded noise on chaotic motion of a triple-well potential system," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 415-424.
    2. Zhen Wang & Lin Wang & Zi-Yu Yin & Cheng-Yi Xia, 2012. "Inferring Reputation Promotes the Evolution of Cooperation in Spatial Social Dilemma Games," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-9, July.
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    Cited by:

    1. Bashkirtseva, I. & Ryashko, L., 2019. "Stochastic sensitivity analysis of chaotic attractors in 2D non-invertible maps," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 78-84.

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