The Dynamics of Sine-Gordon System with Dirichlet Boundary Condition

We prove the existence of the global attractor of Sine-Gordon system with Dirichlet boundary condition and show the attractor is the unique steady state when the damping constant and the diffusion constant are sufficiently large.     

空间离散Fitz-Hugh-Nagumo方程和双稳反应扩散方程组的渐近行为

本文利用扰动方法,研究了Ｆitz-Hugh-Ngaumo方程和双稳反应扩散方程在Neuman边值条件下空间离散后的渐近行为,证明了两个格微分方程组的不变区域、吸引集和整体吸引子的存在性,并给出了离散Ｆitz-Hugh-Ngaumo方程的整体吸引子的Hausdorff维数估计。     

THE ATTRACTORS OF PARTIAL DIFFERENTIAL EQUATIONS

§ 1　 IntroductionThe study of nonlinear dynamics is a fascinating problem which is at the very heartofthe understanding ofmany importantproblems ofthe natural sciences.Infinite dimensionaldynamical systems are very important in nonlinear dynamics.For an infinite dimensionaldynamical system,we mainly study the existence and the structure ofthe attractors.Thereare detailed discussions in [1 ] .Itis especially mentioned there thatthe attractors of gradi-ent systems are of simple structure in s…     

非线性粘弹性柱的稳定性和混沌运动

研究了受轴向周期力作用的各向同性简支柱的动力学稳定性。假定粘弹性材料满足Lea-derman非线性本构关系。导出运动方程为非线性偏微分-积分方程,并利用Galerkin方法简化为非线性微分-积分方程。应用平均法进行了稳定性分析,并用数值结果进行验证。数值结果还表明系统可能存在混沌运动。     

利用比例脉冲控制B-Z反应中混沌的变量选择

自二十世纪七十年代以来 ,混沌现象的研究成为非线性科学中的前沿课题。混沌在其无规律的表面下隐藏着惊人的“秩序”,但在许多情况下 ,混沌属于不利因素 ,因此近年来混沌控制又成为倍受关注的热点 ,出现了各种各样的混沌控制方法。这些混沌控制方法可以分为两大类 ,一类以Ott,Grebogi,Yorke提出的 OGY方法 [1]为代表 ,通过对系统参数实行控制达到混沌控制的目的。另一类以比例脉冲控制法[2 ,3] 为代表 ,由控制系统变量利用系统自身非线性特征实现系统自身反馈达到混沌控制目的。这两类方法各自分别能有效地控制不同特点的混沌系统 ,而比…     

一类 Sine-Gordon 型二阶非线性系统全局吸引子的退化条件及能稳性

本文证明了当｜β｜＜时,有阻尼Sine－Gordon方程的Dirichlet问题的全局吸引子为一个平衡点,而且该平衡点具有指数吸引性,同时将所得结果应用到系统能稳性的研究中．最后给出了若干一般性的结果．     

控制混沌振动的逆系统方法

本文研究了控制混沌振动的逆系统控制。建立了单自由度混沌振动的逆系统控制。以一个呈现混沌姿态运动的航天器动力学模型为例说明了该控制律的应用。最后将该控制律多自由度非线性动系统。     

Double Hopf Bifurcations and Chaos of a Nonlinear Vibration System

A double pendulum system is studied for analyzing the dynamic behaviour near a critical point characterized by nonsemisimple 1:1 resonance. Based on normal form theory, it is shown that two phase-locked periodic solutions may bifurcate from an initial equilibrium, one of them is unstable and the other may be stable for certain values of parameters. A secondary bifurcation from the stable periodic solution yields a family of quasi-periodic solutions lying on a two-dimensional torus. Further cascading bifurcations from the quasi-periodic motions lead to two chaoses via a period-doubling route. It is shown that all the solutions and chaotic motions are obtained under positive damping.     

A Modified Exact Linearization Control for Chaotic Oscillators

The control of chaotic oscillations is investigated in this paper. A control methodology, termed input-output linearization, is modified by locally linearizing the nonlinear control law in the small neighborhood of the control goal. Its suitability for controlling chaotic oscillators is analyzed. The forced Duffing oscillator is treated as a numerical example of controlling chaotic motion to a given fixed point and a given period-2 motion. The control signals and time needed to achieve the desired goals of the modified method are compared with those of the original method. The robustness of the control law is demonstrated.     

非牛顿粘性不可压流方程的近似惯性流形

本文利用对非牛顿粘性不可压缩流方程对时间 t的解析性和长时间渐近性估计 ,具体构造了它的近似惯性流形 ,并得出收敛阶估计 .