具有可变时滞的非线性差分方程的振动性及其应用

利用比较方法和函数的凹凸性讨论了一类具有可变时滞的非线性差分方程振动的问题,得到了一系列的判别准则,推广和改进了已有的结果,并将其应用到了广义Logistic差分方程。     

动力失稳判别准则在非自治系统中的推广

通过假设,将结构动力失稳能量判别准则推广到非自治系统中,总结出在非自治系统中,结构动力失稳的能量判别准则,以此可判断出结构在外部激振荷载作用下(如简谐荷载,脉冲荷载,地震波等)的动力稳定性.     

一类离散非自治竞争系统的绝灭性和稳定性

通过构造适当的Lyapunov绝灭函数,研究了一类离散非自治竞争系统,得到了保证系统中某个种群绝灭和另外一个种群全局吸引的充分性条件,所得的结果补充了前人的工作.     

非自治动力系统中的周期点

引入置换系统的定义.研究非自治动力系统上的自映射顺序改变对动力性质的影响,给出了周期非自治动力系统中周期点的轨迹在其特定置换系统中保持不变得一个充分条件.     

具相似流动的层流边界层方程零解的稳定性分析

二维不可压层流边界层方程,在具相似流动时,可化为Falkner-Skan方程。本文将F-S方程f~(″′)+ff~″+(2m)/(m+1)(1-f~(′2)=0作变量变换,转化成二阶非自治系统,讨论了其零解附近的稳定性,并作了物理解释。     

动词“自主／非自主”语义范畴研究

以语义为基础,针对汉语动词语义范畴中的“自主／非自主”进行对比性研究．通过具体语言实例,从“句法格式区分”、“语义制约性”、“语义特征的相容性和区别性”等方面论述动词“自主与非自主”语义特征,明确“自主”与“非自主”在语义上的对比性及动词的相应语法使用情况．     

Covering relations and Lyapunov condition for topological conjugacy

In this paper, we study stability of non-autonomous discrete dynamical systems. For a two-sided non-autonomous systems with covering relations determined by a transition matrix A, we show that any small C⁰ perturbed system has a sequence of compact invariant sets restricted to which the system is topologically semi-conjugate to σ_A, the two-sided subshift of finite type induced by A. Together with Lyapunov condition of good rate, the semi-conjugacy will become conjugacy. Moreover, if the Lyapunov condition is strict and has perfect rate, then any small C¹ perturbed systems is topological conjugate to σ_A. We also study topological chaos of one-sided systems and systems with limit functions. Lack of hyperbolicity and the time dependence of the rate prevent us from applying classical hyperbolic results or earlier works for autonomous systems: cone condition and Lyapunov function. Two examples are provided to demonstrate the existence of a non-trivial, non-hyperbolic invariant and essential of controlling rate.     

复合材料层合板的多脉冲混沌动力学研究

利用非自治系统的广义Melnikov方法研究了受面内与横向简谐激励共同作用的四边简支复合材料层合矩形板的多脉冲混沌动力学行为。基于含有多个相互耦合非线性项复合材料层合板的二自由度非线性常微分运动控制方程,利用非自治系统的广义Melnikov方法,从理论上证明了复合材料层合板存在多脉冲混沌运动,并根据理论结果作了相应的数值模拟研究,进一步验证了所得出的结论。     

Stabilisation of second-order nonlinear equations with variable delay

For a wide class of second-order nonlinear non-autonomous models, we illustrate that combining proportional state control with the feedback that is proportional to the derivative of the chaotic signal allows to stabilise unstable motions of the system. The delays are variable, which leads to more flexible controls permitting delay perturbations; only delay bounds are significant for stabilisation by a delayed control. The results are applied to the sunflower equation which has an infinite number of equilibrium points.     

Invariant manifolds and control of hyperbolic trajectories on infinite- or finite-time intervals

We consider general non-autonomous systems on infinite- and finite-time intervals and describe some properties of hyperbolic trajectories and their stable and unstable manifolds. Our definitions of hyperbolic trajectories and their stable and unstable manifolds on finite-time intervals are different from one adopted in the previous references, but still possess a desirable property as the previous one. Furthermore, we present numerical methods based on these theoretical results to compute the stable and unstable manifolds, and propose a control method to stabilize unstable hyperbolic trajectories using geometrical structures near them like the Ott, Grebogi and Yorke (OGY) chaos control method. To demonstrate our methods, we give numerical computation results for two examples: a controlled pendulum on infinite- and finite-time intervals and a simple model for a spacecraft transferring from the Earth to the Moon.