Stochastic period-doubling bifurcation analysis of a R?ssler system with a bounded random parameter |
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Authors: | Ni Fei Xu Wei Fang Tong and Yue Xiao-Le |
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Affiliation: | Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China; Department of Engineering Mechanics, Northwestern Polytechnical University, Xi'an 710072, China |
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Abstract: | This paper aims to study the stochastic period-doubling
bifurcation of the three-dimensional R?ssler system with an
arch-like bounded random parameter. First, we transform the
stochastic R?ssler system into its equivalent deterministic one
in the sense of minimal residual error by the Chebyshev polynomial
approximation method. Then, we explore the dynamical behaviour of
the stochastic R?ssler system through its equivalent
deterministic system by numerical simulations. The numerical results
show that some stochastic period-doubling bifurcation, akin to the
conventional one in the deterministic case, may also appear in the
stochastic R?ssler system. In addition, we also examine the
influence of the random parameter intensity on bifurcation
phenomena in the stochastic R?ssler system. |
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Keywords: | Chebyshev polynomial approximation stochastic R?ssler system stochastic period-doubling bifurcation bounded random parameter |
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