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101.
基于线性随机系统Khasminskii球面坐标变换, 计算了谐和激励中含有随机相位的Duffing 方程的最大Lyapunov指数. 依据平均最大Lyapunov指数符号的变化, 分析随机相位对非线性系统动力学行为的影响.说明随机相位可以产生混沌亦可抑制混沌, 从而可以作为混沌控制的一种方法. 结合对相图、Poincaré截面、时间历程图的分析, 说明上述方法是有效的.
关键词:
随机相位
混沌控制
最大Lyapunov指数
Poincaré截面 相似文献
102.
采用一种新方法-反射函数法,建立了非线性非自治微分系统的Poincare映射, 给出了这些微分系统周期解存在及稳定的充要条件. 相似文献
103.
In this paper, we introduce a new concept called ‘a pair of coincident invariant measures’ and establish the existence of coincident invariant measures for set-valued dynamical systems. As applications, we first give the existence of minimal invariant measures (see definition below) for a set-valued mapping, and then set-valued versions of Poincare's recurrence theorems are also derived. 相似文献
104.
Rajaram Nityananda 《Pramana》1979,12(3):257-262
The possibility of extending the well known Poincare sphere representation of polarised light to include phase is considered.
Any attempt to define the zero of phase for each vibration represented on the Poincare sphere runs into discontinuities at
at least one point. These are shown to be inevitable using a topological argument. 相似文献
105.
《数学学报》2014,(6)
<正>on Double Vector Bundles Zhuo CHEN Zhang Ju LIU Yun He SHENG Abstract In this paper,we construct a category of short exact sequences of vector bundles and prove that it is equivalent to the category of double vector bundles.Moreover,operations on double vector bundles can be transferred to operations on the corresponding short exact sequences.In particular,we study the duality theory of double vector bundles in term of 相似文献
106.
粒子在 Hénon-Heiles势中的逃逸动力学模拟 总被引:1,自引:1,他引:0
利用庞加莱截面和相空间轨迹方法对粒子在Hénon-Heiles势中的逃逸动力学进行了模拟.粒子的动力学性质敏感地依赖于粒子的能量.数值计算表明当能量很小时,粒子的运动是规则的;随着能量的增加,粒子的运动开始出现混沌.当能量增加到鞍点能Es时,几乎所有的相空间轨迹都是混沌的.当粒子的能量E>Es,粒子可以越过势阱发生逃逸.对于给定的大于Es的能量, 我们画出了粒子的逃逸-时间曲线和逃逸轨迹.我们的研究对于研究混沌传输和逃逸动力学具有一定的参考价值. 相似文献
107.
Mehmet Pakdemirli Mustafa Mehmet Fatih Karahan 《Mathematical Methods in the Applied Sciences》2010,33(6):704-712
The new perturbation algorithm combining the method of multiple scales (MS) and Lindstedt–Poincare techniques is applied to an equation with quadratic and cubic nonlinearities. Approximate analytical solutions are found using the classical MS method and the new method. Both solutions are contrasted with the direct numerical solutions of the original equation. For the case of strong nonlinearities, solutions of the new method are in good agreement with the numerical results, whereas the amplitude and frequency estimations of classical MS yield high errors. For strongly nonlinear systems, exact periods match well with the new technique while there are large discrepancies between the exact and classical MS periods. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
108.
We give a stereological version of the Gauss–Bonnet formula in order to compute the Euler characteristic of a domain with boundary in a smooth orientable surface in 3, by looking at contacts with a 'sweeping' plane. 相似文献
109.
设r为一个正实数,1<r<2,是一个H-群,v:Γ→C是一个乘子系(定义见§1).在本文中我们定义了所谓非解析的Poincare级数P_(nr)(z,s,v,A_j,Γ,k_j)(§2),求出了它的Fourier展开式,应用Laplacian算子的谱及Selberg的Zeta函数,我们证明了P_(nr)(z,s,v,A_j,Γ,k_j)可以解析延拓到包含s=0的一个半平面Re(s)>一δ中去。从而为我们研究解析Poincare级数作好了准备。 相似文献
110.
Qinsheng Bi 《International Journal of Non》2004,39(1):33-54
The dynamical behavior of two coupled parametrically excited van der pol oscillators is investigated in this paper. Based on the averaged equations, the transition boundaries are sought to divide the parameter space into a set of regions, which correspond to different types of solutions. Two types of periodic solutions may bifurcate from the initial equilibrium. The periodic solutions may lose their stabilities via a generalized static bifurcation, which leads to stable quasi-periodic solutions, or via a generalized Hopf bifurcation, which leads to stable 3D tori. The instabilities of both the quasi-periodic solutions and the 3D tori may directly lead to chaos with the variation of the parameters. Two symmetric chaotic attractors are observed and for certain values of the parameters, the two attractors may interact with each other to form another enlarged chaotic attractor. 相似文献