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随机Duffing单边约束系统的倍周期分岔

ISSN号：1000-3290
期刊名称：《物理学报》
时间：0
分类：O415.5[理学—理论物理;理学—物理]
作者机构：[1]西北工业大学理学院应用数学系,西安710072, [2]陕西师范大学数学系,西安710062
相关基金：国家自然科学基金（批准号10472091,10332030,10502042）资助的课题.

关键词：非光滑动力系统, 随机Duffing系统, Chebyshev多项式, 倍周期分岔, non-smooth dynamic system, stochastic Duffing system, Chebyshev polynomial, period-doubling bifurcation

中文摘要：

通过引进平均约束面和平均跃变方程对随机约束系统的约束条件进行处理，把研究随机光滑系统倍周期分岔的Chebyshev多项式逼近的方法运用到随机非光滑系统中，数值研究表明随机Duffing单边约束系统同样存在丰富的倍周期分岔现象，Chebyshev多项式逼近是研究带有约束的随机非光滑动力系统的有效方法．

英文摘要：

The conditions of constraint are treated by means of the mean constraint plane and the mean jump equation, in which the method of the Chebyshev polynomial approximation, previously used to explore period-doubling bifurcation of stochastic smooth systems, is applied to stochastic non-smooth systems. Numerical simulations show that period-doubling bifurcation exists in stochastic Duffing one-sided constraint system just as in smooth stochastic Duffing system, and furthermore, the Chebyshev polynomial approximation is an effective method in exploring the dynamical behavior of stochastic non-smooth system.

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