渐近稳定的

It is proved that, when the value of critical threshold less than 1, the disease free equilibrium point is globally asymptotically stable. Further more, Bursaphelenchtis Xylophilus is used to construct the Lyapunov function, and the stability theory of Lyapunov function is used to prove that the equilibrium point is Global asymptotic stable. It explains that the Bursaphelenchus Xylophilus wiil eventually disappear.

证明了当临界阈值小于1时，无病平衡点是局部渐近稳定的，进一步利用巴尔巴欣公式构造Lyapunov函数，运用Lyapunov稳定性理论证明了该平衡点的全局渐近稳定性，说明松材线虫病会最终消失；当临界阈值大于1时，病虫害平衡点是局部渐近稳定的。

This paper consists of three parts: Firstly, we discuss a nonautonomous -species two-patches cooperative Lotka-Volterra diffusion system. Using Brouwer fixed-point theory and Liapunov function, under some conditions, we obtain that the system has a unique globally asymptotically stable positive periodic solution. Secondly, we consider a kind of nonautonomous predator-prey model, in which preys are with stage structure and the predator are with two patches.

中文摘要：本文分三部分讨论三类生态模型周期解或概周期解的存在性及全局渐近稳定性等内容：第一部分讨论了两斑块种群的互惠Lotka-Volterra扩散系统，运用不动点理论和构造Liapunov函数，得到了系统存在唯一一个全局渐近稳定的正周期解的充分条件。

In this paper, we discuss asymptotically stable sets of graph maps and give a necessary and sufficient condition for a fixed point of f to be asymptotically stable.

在本文中，我们讨论了图映射的渐近稳定集，并给出了f的不动点为渐近稳定的一个充分必要条件。

By analysis of such models, a method, which is used to find out the region of convergence and to study the local stability for strong nonlinear system, are derived. Thus, we can consider the strong nonlinear neural networks using such method.

利用新的比较方法，考虑了具变时滞和常恢复率的同质人群HIV梯度传染病模型，得到了一个阈值，当阈值小于1时，疾病消除平衡点全局指数渐近稳定，当阈值大于1时，传染病平衡点存在唯一，同时得到该传染病平衡点局部指数渐近稳定的充分条件。

When the value of critical threshold larger than 1, the disease and insect pests equilibrium point is locally asymptotically stable An appropriate Dulac function should be choosed and Bendixson-Dulac creterion is used to prove that the limit cycle in this model does not exist. It explains that the disease and insect pests equilibrium point is globally asymptotically stable.

选取适当的Dulac函数，利用Bendixson-Dulac判别法证明了极限环的不存在性，说明局部渐近稳定的病虫害平衡点也全局渐近稳定。

For delay discrete-time linear system, saturant function is introduced. Thesufficient condition of GAS and RAS is presented by saturant function infimum.

针对时滞离散线性系统，引入饱和函数，利用饱和函数的下确界，建立了系统全局渐近稳定和局部渐近稳定的充分条件。

The deduced integral invariant is employed to study the 3D predator-prey Lotka-Volterra systems and some new results are obtained.

利用此积分不变量，对三维捕食被捕食 LVS解的渐近性进行讨论，得到了平衡点全局渐近稳定的新条件，推广了已有LVS正平衡点全局渐近稳定的结

In this paper,we study the existence.uniqueness and asymptotic stability of the periodic solutions for a class of nonautonomous systems by using the method of Liapunov Function.

利用Liapunov函数方法，研究了一类非自治系统周期解的存在唯一性及渐近稳定性，得到了存在唯一渐近稳定的周期解的充分条件。

In this thesis, some theories and approaches related to continuous dynamics, discrete dynamics, impulsive dynamics, operator theory and numerical simulations are used to investigate dynamical behaviors including the existence and globally asymptotic stability of periodic solutions, permanence, extinction, and all kinds of complexities, and meanwhile the possible effects of delay and impulse on the dynamical behaviors are discussed.

我们的这些结果显示出这三个时滞周期系统正周期解存在且全局渐近稳定的充分条件在形式上几乎能够很好的与相应的无时滞自治系统正平衡态存在且全局渐近稳定的充分条件相对(来源：A5babBC论文网www.abclunwen.com)应，这些结果也显示了时滞对系统正周期解的存在性和全局渐近稳定性是有影响的，它们推广并改进了一些已有的相关结果。

Last we obtain globally asymptotically stability of boundary equilibrium by applying locally asymptotically stability and attractiveness and persistence by using uniform repeller theorem.

在第二章中研究了一类具有时滞的捕食与被捕食系统，分析了系统的正不变集，运用了特征值理论得到了边界平衡点性质，当时滞很小时，得到了系统在正平衡点局部渐近稳定的充分条件，以及当T增加到T_0时，系统在正平衡点附近产生Hopf分支的充分条件；利用局部渐近稳定性加吸引性得到了边界平衡点全局渐近稳定性的充分条件，且应用一致排斥定理得到了种群持久生存的条件。

Objective: To study the effect of polycythemia on blood oxygen saturation.

裴蕾目的：观察RBC剧增而引起的高粘血症对血氧饱和度的影响。

Based on SIMPLER algorithm in the curvilinear body-fitted coordinates, the calculations were performed for Pr=0.7, Re=10~1000 on non-orthogonal non-staggered grids which are generated by elliptic equation systems.

采用曲线坐标系下压力与速度耦合的SIMPLER算法，数值研究了周期性渐扩渐缩波纹通道内脉动流动与换热情况，流动Re数的范围为10~1000，Pr数为0.7。