Stochastic period-doubling bifurcation analysis of stochastic Bonhoeffer-van der Pol system  

作　　者：张莹 徐伟 方同 徐旭林 

机构地区：[1]Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China [2]ibration Research Centre, Northwestern Polytechnlcal University, Xi'an 710072, China [3]Department of Automation, Nankai University, Tianjin 300071, China

出　　处：《Chinese Physics B》2007年第7期1923-1933,共11页中国物理B（英文版）

基　　金：Project supported by the Major Program of the National Natural Science Foundation of China, China （Grant No 10332030）, the National Natural Science Foundation of China （Grant No 10472091）, and the Graduate Starting Seed Fund of Northwestern Polytechnical University, China （Grant No Z200655）.

摘　　要：In this paper, the Chebyshev polynomial approximation is applied to the problem of stochastic period-doubling bifurcation of a stochastic Bonhoeffer-van der Pol （BVP for short） system with a bounded random parameter. In the analysis, the stochastic BVP system is transformed by the Chebyshev polynomial approximation into an equivalent deterministic system, whose response can be readily obtained by conventional numerical methods. In this way we have explored plenty of stochastic period-doubling bifurcation phenomena of the stochastic BVP system. The numerical simulations show that the behaviour of the stochastic period-doubling bifurcation in the stochastic BVP system is by and large similar to that in the deterministic mean-parameter BVP system, but there are still some featured differences between them. For example, in the stochastic dynamic system the period-doubling bifurcation point diffuses into a critical interval and the location of the critical interval shifts with the variation of intensity of the random parameter. The obtained results show that Chebyshev polynomial approximation is an effective approach to dynamical problems in some typical nonlinear systems with a bounded random parameter of an arch-like probability density function.In this paper, the Chebyshev polynomial approximation is applied to the problem of stochastic period-doubling bifurcation of a stochastic Bonhoeffer-van der Pol （BVP for short） system with a bounded random parameter. In the analysis, the stochastic BVP system is transformed by the Chebyshev polynomial approximation into an equivalent deterministic system, whose response can be readily obtained by conventional numerical methods. In this way we have explored plenty of stochastic period-doubling bifurcation phenomena of the stochastic BVP system. The numerical simulations show that the behaviour of the stochastic period-doubling bifurcation in the stochastic BVP system is by and large similar to that in the deterministic mean-parameter BVP system, but there are still some featured differences between them. For example, in the stochastic dynamic system the period-doubling bifurcation point diffuses into a critical interval and the location of the critical interval shifts with the variation of intensity of the random parameter. The obtained results show that Chebyshev polynomial approximation is an effective approach to dynamical problems in some typical nonlinear systems with a bounded random parameter of an arch-like probability density function.

关 键 词：Chebyshev polynomial approximation stochastic Bonhoeffer-van der Pol system stochastic period-doubling bifurcation bounded random parameter 

分 类 号：O242[理学—计算数学]