共查询到14条相似文献,搜索用时 109 毫秒
1.
应用 Chebyshev 多项式逼近法研究了谐和激励作用下具有随机参数的随机van der Pol系统 的倍周期分岔现象.随机系统首先被转化成等价的确定性系统,然后通过数值方法求得响应 ,借此探索了随机van der Pol系统丰富的随机倍周期分岔现象.数值模拟显示随机van der Pol 系统存在与确定性系统极为相似的倍周期分岔行为,但受随机因素的影响,又有与之不 同之处.数值结果表明,Chebyshev 多项式逼近是研究非线性系统动力学问题的一种新的有 效方法.
关键词:
Chebyshev 多项式
随机van der Pol 系统
倍周期分岔 相似文献
2.
3.
讨论简谐激励作用下含有界随机参数的双势阱Duffing-van der Pol系统的倍周期分岔现象.首先用Chebyshev 多项式逼近法将随机Duffing-van der Pol系统化成与其等价的确定性系统,然后通过等价确定性系统来探索该系统的倍周期分岔现象.数值模拟显示随机Duffing-van der Pol 系统与均值参数系统有着类似的倍周期分岔行为,同时指出,随机参数系统的倍周期分岔有其自身独有的特点.文中的主要数值结果表明Chebyshev 多项式逼近法是研究非线性随机参数系统动力学问题的一种有效方法.
关键词:
Chebyshev多项式
随机Duffing-van der Pol系统
倍周期分岔 相似文献
4.
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.
关键词:
随机van der Pol系统
Hopf分岔
正交多项式逼近 相似文献
5.
讨论了具有有界随机参数的随机Bonhoeffer-Van der Pol系统的随机混沌现象,并利用噪声对其进行控制.首先运用Chebyshev多项式逼近的方法,将随机Bonhoeffer-Van der Pol系统转化为等价的确定性系统,使原系统的随机混沌控制问题转换为等价的确定性系统的确定性混沌控制问题,继而可用Lyapunov指数指标来研究等价确定性系统的确定性混沌现象和控制问题.数值结果表明,随机Bonhoeffer-Van der Pol系统的随机混沌现象与相应的确定性Bonhoeffer-Van der Pol系统极为相似.利用噪声控制法可将混沌控制到周期轨道,但是在随机参数及其强度的影响下也呈现出一些特点. 相似文献
6.
7.
研究了Lévy稳定噪声激励下的双稳Duffing-van der Pol振子,利用Monte Carlo方法,得到了振幅的稳态概率密度函数.分析了Lévy稳定噪声的强度和稳定指数对概率密度函数的影响,通过稳态概率密度的性质变化,讨论了噪声振子的随机分岔现象,发现了不仅系统参数和噪声强度可以视为分岔参数,Lévy噪声的稳定指数 α 的改变也能诱导系统出现随机分岔现象.
关键词:
Lévy稳定噪声
Duffing-van der Pol振子
稳态概率密度函数
随机分岔 相似文献
8.
应用Laguerre正交多项式逼近法研究了含有随机参数的双势阱Duffing系统的分岔和混沌行为.系统参数为指数分布随机变量的非线性动力系统首先被转化为等价的确定性扩阶系统,然后通过数值方法求得其响应.数值模拟结果的比较表明,含有随机参数的双势阱Duffing系统保持着与确定性系统相类似的倍周期分岔和混沌行为,但是由于随机因素的影响,在局部小区域内随机参数系统的动力学行为会发生突变.
关键词:
双势阱Duffing系统
指数分布概率密度函数
Laguerre多项式逼近
随机分岔 相似文献
9.
对含有两个时滞参数、受简谐激励作用下的van der Pol-Duffing方程进行了研究,着重研究了时滞参数对该类参数激励系统的主共振的分岔响应控制.首先采用摄动法从理论上推导出时滞动力系统的分岔响应方程,用奇异性理论得到了退化余维一分岔和余维二分岔的条件,以及Hopf分岔的存在性及发生该分岔的条件,最后用数值模拟的方法研究了时滞参数对系统分岔响应的影响.研究结果表明,适当选取时滞参数,不仅可以改变分岔响应曲线的拓扑形态, 还可以改变分岔点的位置.
关键词:
摄动法
分岔控制
时滞动力系统 相似文献
10.
针对一类多项式形式的Hopf分岔系统, 提出了一种鲁棒稳定的控制器设计方法. 使用该方法设计控制器时不需要求解出系统在分岔点处的分岔参数值, 只需要估算出分岔参数的上下界, 然后设计一个参数化的控制器, 并通过Hurwitz判据和柱形代数剖分技术求解出满足上下界条件的控制器参数区域, 最后在得到的这个区域内确定出满足鲁棒稳定的控制器参数值. 该方法设计的控制器是由包含系统状态的多项式构成, 形式简单, 具有通用性, 且添加控制器后不会改变原系统平衡点的位置. 本文首先以Lorenz系统为例说明了控制器的推导和设计过程, 然后以van der Pol振荡系统为例, 进行了工程应用. 通过对这两个系统的控制器设计和仿真, 说明了文中提出的控制器设计方法能够有效地应用于这类Hopf分岔系统的鲁棒稳定控制, 并且具有通用性. 相似文献
11.
Stochastic period-doubling bifurcation analysis of stochastic Bonhoeffer--van der Pol system 总被引:2,自引:0,他引:2 下载免费PDF全文
In this paper, the Chebyshev polynomial approximation is applied to
the problem of stochastic period-doubling bifurcation of a stochastic
Bonhoeffer--van der Pol (BVP for short) system with a bounded random
parameter. In the analysis, the stochastic BVP system is transformed
by the Chebyshev polynomial approximation into an equivalent
deterministic system, whose response can be readily obtained by
conventional numerical methods. In this way we have explored plenty
of stochastic period-doubling bifurcation phenomena of the stochastic
BVP system. The numerical simulations show that the behaviour of the
stochastic period-doubling bifurcation in the stochastic BVP system
is by and large similar to that in the deterministic mean-parameter
BVP system, but there are still some featured differences between
them. For example, in the stochastic dynamic system the
period-doubling bifurcation point diffuses into a critical interval
and the location of the critical interval shifts with the variation
of intensity of the random parameter. The obtained results show that
Chebyshev polynomial approximation is an effective approach to
dynamical problems in some typical nonlinear systems with a bounded
random parameter of an arch-like probability density function. 相似文献
12.
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
13.
Stochastic period-doubling bifurcation analysis of a Rssler system with a bounded random parameter 下载免费PDF全文
This paper aims to study the stochastic period-doubling bifurcation of the three-dimensional Rssler system with an arch-like bounded random parameter. First, we transform the stochastic Rssler system into its equivalent deterministic one in the sense of minimal residual error by the Chebyshev polynomial approximation method. Then, we explore the dynamical behaviour of the stochastic Rssler system through its equivalent deterministic system by numerical simulations. The numerical results show that some stochastic period-doubling bifurcation, akin to the conventional one in the deterministic case, may also appear in the stochastic Rssler system. In addition, we also examine the influence of the random parameter intensity on bifurcation phenomena in the stochastic Rssler system. 相似文献
14.
Stochastic period-doubling bifurcation analysis of a R?ssler system with a bounded random parameter 下载免费PDF全文
This paper aims to study the stochastic period-doubling
bifurcation of the three-dimensional R?ssler system with an
arch-like bounded random parameter. First, we transform the
stochastic R?ssler system into its equivalent deterministic one
in the sense of minimal residual error by the Chebyshev polynomial
approximation method. Then, we explore the dynamical behaviour of
the stochastic R?ssler system through its equivalent
deterministic system by numerical simulations. The numerical results
show that some stochastic period-doubling bifurcation, akin to the
conventional one in the deterministic case, may also appear in the
stochastic R?ssler system. In addition, we also examine the
influence of the random parameter intensity on bifurcation
phenomena in the stochastic R?ssler system. 相似文献