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Stochastic Bifurcations of a Fractional-Order Vibro-Impact Oscillator Subjected to Colored Noise Excitation

Ya-Hui Sun

School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, P. R. China

E-mail Address: yahsun@163.com

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Yong-Ge Yang

https://orcid.org/0000-0001-7791-583X

School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, P. R. China

E-mail Address: yonggeyang@163.com

Corresponding author.

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Ling Hong

State Key Laboratory for Strength and Vibration, Xi’an Jiaotong University, Xi’an 710049, P. R. China

E-mail Address: hongling@mail.xjtu.edu.cn

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, and

Wei Xu

Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710129, P. R. China

E-mail Address: weixu@nwpu.edu.cn

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https://doi.org/10.1142/S0218127421501777Cited by:3 (Source: Crossref)

Abstract

A stochastic vibro-impact system has triggered a consistent body of research work aimed at understanding its complex dynamics involving noise and nonsmoothness. Among these works, most focus is on integer-order systems with Gaussian white noise. There is no report yet on response analysis for fractional-order vibro-impact systems subject to colored noise, which is presented in this paper. The biggest challenge for analyzing such systems is how to deal with the fractional derivative of absolute value functions after applying nonsmooth transformation. This problem is solved by introducing the Fourier transformation and deriving the approximate probabilistic solution of the fractional-order vibro-impact oscillator subject to colored noise. The reliability of the developed technique is assessed by numerical solutions. Based on the theoretical result, we also present the critical conditions of stochastic bifurcation induced by system parameters and show bifurcation diagrams in two-parameter planes. In addition, we provide a stochastic bifurcation with respect to joint probability density functions. We find that fractional order, coefficient of restitution factor and correlation time of colored noise excitation can induce stochastic bifurcations.

Keywords:

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