Analysis of stochastic bifurcation and chaos in stochastic Duffing--van der Pol system via Chebyshev polynomial approximation
Ma Shao-Juan (马少娟)ab, Xu Wei (徐伟)a, Li Wei (李伟)a, Fang Tong (方同)a
a Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China; b Department of Information & Computation Sciences, the Second Northwest University for Nationalities, Yinchuan 750021, China
Abstract The Chebyshev polynomial approximation is applied to investigate the stochastic period-doubling bifurcation and chaos problems of a stochastic Duffing--van der Pol system with bounded random parameter of exponential probability density function subjected to a harmonic excitation. Firstly the stochastic system is reduced into its equivalent deterministic one, and then the responses of stochastic system can be obtained by numerical methods. Nonlinear dynamical behaviour related to stochastic period-doubling bifurcation and chaos in the stochastic system is explored. Numerical simulations show that similar to its counterpart in deterministic nonlinear system of stochastic period-doubling bifurcation and chaos may occur in the stochastic Duffing--van der Pol system even for weak intensity of random parameter. Simply increasing the intensity of the random parameter may result in the period-doubling bifurcation which is absent from the deterministic system.
Received: 23 June 2005
Revised: 16 March 2006
Accepted manuscript online:
Fund: Project supported by the National Natural Science Foundation of China (Grants Nos 10472091 and 10332030).
Cite this article:
Ma Shao-Juan (马少娟), Xu Wei (徐伟), Li Wei (李伟), Fang Tong (方同) Analysis of stochastic bifurcation and chaos in stochastic Duffing--van der Pol system via Chebyshev polynomial approximation 2006 Chinese Physics 15 1231
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