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11.
Analysis of stochastic bifurcation and chaos in stochastic Duffing--van der Pol system via Chebyshev polynomial approximation 下载免费PDF全文
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. 相似文献
12.
研究了由乘性白噪声和加性白噪声驱动的非对称双稳系统中,势阱的非对称性对两个不同方 向的平均首次穿越时间的影响.发现在非对称双稳系统中,两个不同方向的平均首次穿越时 间是与初始状态有关.此外,对一维非对称达芬模型的平均首次穿越时间进行了研究.数值结 果表明:(1) 非对称双稳系统的平均首次穿越时间对初始状态有“记忆性”;(2) 噪声强度 对两个不同方向的平均首次穿越时间T+(xs1→xs2)和 T-(xs2→xs1)的影响是不同的:lnT--D 曲线上存在峰值,出 现了“共振”现象,而lnT+-D曲线是单调的;(3) 势阱的非对称性r对T +(xs1→xs2)和T-(xs2→xs1 )的影响是不 同的:lnT--r曲线上存在极小值,出现了“抑制”现象,而lnT+ -r曲线是单调的.
关键词:
平均首次穿越时间
非对称双稳系统
乘性噪声
加性噪声 相似文献