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中国物理学会期刊

一类随机van der Pol系统的Hopf 分岔研究

CSTR: 32037.14.aps.60.010502

Hopf bifurcation in a kind of stochastic van der Pol system

CSTR: 32037.14.aps.60.010502
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  • 研究了一类随机van der Pol 系统的Hopf分岔行为.首先根据Hilbert空间的正交展开理论,含有随机参数的van der Pol系统被约化为等价确定性系统,然后利用确定性分岔理论分析了等价系统的Hopf分岔,得出了随机van der Pol 系统的Hopf 分岔临界点,探究了随机参数对系统Hopf分岔的影响.最后利用数值模拟验证了理论分析结果.

     

    The Hopf bifurcation of van der Pol system with random parameter is studied. Firstly according to the orthogonal polynomial approximation in Hilbert space, the van der Pol system with random parameter can be reduced into the equivalent deterministic system. Then the Hopf bifurcation can be explored by the traditional methods in deterministic bifurcation theory. After the critical point of Hopf bifurcation in stochastic van der Pol system is obtained, the influence of the random parameter on Hopf bifurcation in stochastic van der Pol system is analyzed. At last we verified these results by numerical simulations.

     

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