随机Duffing-van der Pol系统响应的Chebyshev多项式逼近被引量：1

THE ORTHOGONAL POLYNOMICAL APPROXIMATION FOR RESPONSE PROBLEM OF STOCHASTIC DUFFING-VAN DER POL SYSTEM

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摘要对一类含随机参数的Duffing-vanderPol系统,运用Chebyshev多项式逼近法,将其转化成等价的确定性扩阶系统;通过求解等价系统在谐和激励下的稳态响应,可得Duffing-vandetPol系统相应的稳态随机响应,研究了当谐和激励的振幅变化时,含随机参数的Duffing-vanderPol系统的对称破裂分岔和倍周期分岔.数值模拟结果与数值解比较表明:正交多项式逼近法能有效地解决此类非线性随机动力系统的响应问题. The Chebyshev polynomial approximation was applied to the dynamical response problem of the stochastic Duffing-van der Pol system with random parameters. First,the stochastic Duffing-van der Pol system was reduced into an equivalent deterministic one for substitution. Then, the response of the stochastic Duffing-van der Pol system can be obtained by numerical methods for this equivalent deterministic system. Moreover, the symmetry-breaking bifurcation and period-doubling bifurcation of the stochastic Duffing- van der Pol system were presented while the excitation frequency vary. Numerical simulation implies that the proposed method is a new effective approach to dynamical responses of stochastic nonlinear systems.

作者马少娟徐伟雷佑铭

机构地区西北工业大学应用数学系

出处《动力学与控制学报》 2004年第3期80-84,共5页 Journal of Dynamics and Control

基金国家自然科学基金资助项目(10332030)~~

关键词摄动法动力响应随机Duffing-vander Pol系统 CHEBYSHEV多项式动力系统对称破裂分岔倍周期分岔 Chebyshev polynomial,stochastic Duffing-van der Pol system,symmetry-breaking bifurcation,period-doubling bifurcation

分类号 O324 [理学—一般力学与力学基础]

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