%0 Journal Article
%T Period-doubling bifurcation analysis of stochastic van der Pol system via Chebyshev polynomial approximation<br>基于Chebyshev多项式逼近的随机 van der Pol系统的倍周期分岔分析
%A Ma Shao-Juan
%A Xu Wei
%A Li Wei
%A Jin Yan-Fei
%A <br>马少娟
%A 徐 伟
%A 李 伟
%A 靳艳飞
%J 物理学报
%D 2005
%I 
%X Chebyshev polynomial approximation is applied to the period-doubling bifurcation problem of a stochastic van der Pol system with bounded random parameters and subjected to harmonic excitations. Firstly, the stochastic system is reduced to its equivalent deterministic one, through which the response of the stochastic s ystem can be obtained by numerical methods. Nonlinear dynamical behavior related to various forms of stochastic period-doubling bifurcation in the stochastic sy stem is explored. Numerical simulations show that similar to their counterpart i n deterministic nonlinear system, various forms of period-doubling bifurcation m ay occur in the stochastic van der Pol system, but with some modified features. Numerical results also show that Chebyshev polynomial approximation can provide an effective approach to dynamical problems in stochastic nonlinear systems.
%K Chebyshev polynomial
%K stochastic van der Pol system
%K period-doubling bifurcation<br>Chebyshev
%K 多项式
%K 随机van
%K der
%K Pol
%K 系统
%K 倍周期分岔
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=47EA7CFDDEBB28E0&jid=29DF2CB55EF687E7EFA80DFD4B978260&aid=3A3D147F86C99410&yid=2DD7160C83D0ACED&vid=318E4CC20AED4940&iid=5D311CA918CA9A03&sid=E0322A8ACAE9818B&eid=E0B17D28B6991BBF&journal_id=1000-3290&journal_name=物理学报&referenced_num=0&reference_num=20