Analysis of stochastic bifurcation and chaos in stochastic Duffing–van der Pol system via Chebyshev polynomial approximation
Analysis of stochastic bifurcation and chaos in stochastic Duffing–van der Pol system via Chebyshev polynomial approximation
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DOI：
10.1088/1009-1963/15/6/017
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发表时间：
2006-06
期刊：
影响因子：
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通讯作者：
Shao-Juan Ma;Xu Wei;Li Wei;Fang Tong
中科院分区：
文献类型：
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作者：
Shao-Juan Ma;Xu Wei;Li Wei;Fang Tong
应用切比雪夫多项式近似研究谐波激励下具有指数概率密度函数有界随机参数的随机 Duffing-van der Pol 系统的随机倍周期分岔和混沌问题。首先将随机系统简化为其等效的确定性系统，然后通过数值方法获得随机系统的响应。探讨了与随机系统中的随机倍周期分岔和混沌相关的非线性动力学行为。数值模拟表明，即使随机参数强度较弱，随机 Duffing-van der Pol 系统也可能出现与确定性非线性系统中的随机倍周期分岔和混沌类似的现象。简单地增加随机参数的强度可能会导致确定性系统中不存在的倍周期分岔。
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.