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Stochastic period-doubling bifurcation analysis of a Rössler system with a bounded random parameter |
Ni Fei(倪菲)a)†, Xu Wei(徐伟)a), Fang Tong(方同)b), and Yue Xiao-Le(岳晓乐) a) |
a Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China; b 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 Rössler system with an arch-like bounded random parameter. First, we transform the stochastic Rössler 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 Rössler 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 Rössler system. In addition, we also examine the influence of the random parameter intensity on bifurcation phenomena in the stochastic Rössler system.
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Received: 26 May 2009
Revised: 20 July 2009
Accepted manuscript online:
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PACS:
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05.45.Pq
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(Numerical simulations of chaotic systems)
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02.10.De
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(Algebraic structures and number theory)
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02.30.Mv
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(Approximations and expansions)
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02.30.Oz
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(Bifurcation theory)
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02.50.Ey
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(Stochastic processes)
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05.40.-a
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(Fluctuation phenomena, random processes, noise, and Brownian motion)
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Fund: Project supported by the National
Natural Science Foundation of China (Grant No. 10872165). |
Cite this article:
Ni Fei(倪菲), Xu Wei(徐伟), Fang Tong(方同), and Yue Xiao-Le(岳晓乐) Stochastic period-doubling bifurcation analysis of a Rössler system with a bounded random parameter 2010 Chin. Phys. B 19 010510
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