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Stochastic P-bifurcation analysis of a novel type of unilateral vibro-impact vibration system

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  • Qian, Jiamin
  • Chen, Lincong

Abstract

This work investigated the stochastic P-bifurcation (SPB) of a new class of unilateral impact vibration (VI) system under random parametric excitations, in which the elastoplastic stage of impact process is described by the restitution coefficient dependent with velocity model. By dint of the transformation of non-smooth, a new system without impact could be transformed from the original VI system. Subsequently, the stationary probability density functions (PDFs) of new system could be calculated by the associated equivalent nonlinear system. And then the critical parameters condition of SPB could be derived by means of the catastrophe theory. In the course of the study, it is verified that the new parameters induce the bifurcation of the system, which can be used to accurately measure the bifurcation behavior of the system quantitatively. And the system will tend to be stable under the precondition of enhancing the noise intensity. In addition, the validation of analytical results is examined by relative figures.

Suggested Citation

  • Qian, Jiamin & Chen, Lincong, 2021. "Stochastic P-bifurcation analysis of a novel type of unilateral vibro-impact vibration system," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).
    • Handle: RePEc:eee:chsofr:v:149:y:2021:i:c:s0960077921004665
    DOI: 10.1016/j.chaos.2021.111112
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    References listed on IDEAS

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    1. Yong-Ge Yang & Ya-Hui Sun & Wei Xu, 2019. "Stochastic Bifurcations of a Fractional-Order Vibro-Impact System Driven by Additive and Multiplicative Gaussian White Noises," Complexity, Hindawi, vol. 2019, pages 1-10, October.
    2. Han, Ping & Wang, Liang & Xu, Wei & Zhang, Hongxia & Ren, Zhicong, 2021. "The stochastic P-bifurcation analysis of the impact system via the most probable response," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. Li, Bo & Liang, Houjun & He, Qizhi, 2021. "Multiple and generic bifurcation analysis of a discrete Hindmarsh-Rose model," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    4. Bilazeroğlu, Ş. & Merdan, H., 2021. "Hopf bifurcations in a class of reaction-diffusion equations including two discrete time delays: An algorithm for determining Hopf bifurcation, and its applications," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
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    Cited by:

    1. Bashkirtseva, Irina & Ryashko, Lev, 2022. "Stochastic generation and shifts of phantom attractors in the 2D Rulkov model," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    2. Li, Wei & Zhang, Ying & Huang, Dongmei & Rajic, Vesna, 2022. "Study on stationary probability density of a stochastic tumor-immune model with simulation by ANN algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

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