中国物理B ›› 2010, Vol. 19 ›› Issue (1): 10510-10510.doi: 10.1088/1674-1056/19/1/010510

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Stochastic period-doubling bifurcation analysis of a R?ssler system with a bounded random parameter

倪菲1, 徐伟1, 岳晓乐1, 方同2   

  1. (1)Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China; (2)Department of Engineering Mechanics, Northwestern Polytechnical University, Xi'an 710072, China
  • 收稿日期:2009-05-26 修回日期:2009-07-20 出版日期:2010-01-15 发布日期:2010-01-15
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 10872165).

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)   

  1. a Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China; b Department of Engineering Mechanics, Northwestern Polytechnical University, Xi'an 710072, China
  • Received:2009-05-26 Revised:2009-07-20 Online:2010-01-15 Published:2010-01-15
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 10872165).

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摘要： 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.

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.

Key words: Chebyshev polynomial approximation, stochastic Rössler system, stochastic period-doubling bifurcation, bounded random parameter

中图分类号:  (Numerical simulations of chaotic systems)

  • 05.45.Pq
02.10.De (Algebraic structures and number theory) 02.30.Mv (Approximations and expansions) 02.30.Oz (Bifurcation theory) 02.50.Ey (Stochastic processes) 05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion)