一类非线性时滞离散系统的渐近行为（英文）

本文研究了一类二维时滞非线性差分系统.利用稳定性理论和最优控制理论等方法,本文首先获得了保证正平衡点的存在唯一以及全局渐近稳定的充分条件;然后对消费函数的最大化的最优控制问题进行讨论,获得了最优解的存在性与稳定性条件;最后,通过数值模拟验证了结果的有效性.本文推广了一维时滞非线性差分系统中给出的相关结论.     

一类带有接种的流行病模型的全局稳定性

该文讨论了一类带有接种的流行病模型. 在该模型中假设恢复后的个体与被接种的个体均具有确定的免疫期, 它是一个时滞微分系统. 通过分析, 得到了地方病平衡点存在的阈值, 以及无病平衡点和地方病平衡点局部渐近稳定和全局渐近稳定的充分条件.     

一类随机惯性时滞神经网络的稳定性北大核心

研究一类随机惯性时滞神经网络稳定性问题.通过引入适当变量变换将二阶微分系统转换为一阶微分系统,利用同胚映射,Ito公式和微分算子,构造恰当的Lyapunov函数和采用递推归纳,给出其系统平衡点存在唯一及全局渐近稳定和解指数稳定判定的充分条件,最后通过数值模拟例子说明所得理论结果的正确性.     

多物种竞争差分系统正周期解的存在性

本利用Mawhin的重合度理论研究了一类多物种竞争差分系统正周期解的存在性，获得了保证该差分系统存在正周期解的新的充分条件．     

一类随机惯性时滞神经网络的稳定性

研究一类随机惯性时滞神经网络稳定性问题.通过引入适当变量变换将二阶微分系统转换为一阶微分系统,利用同胚映射, It?公式和微分算子,构造恰当的Lyapunov函数和采用递推归纳,给出其系统平衡点存在唯一及全局渐近稳定和解指数稳定判定的充分条件,最后通过数值模拟例子说明所得理论结果的正确性.     

带有分段常数变量的Lorenz系统的稳定性和分支

本文研究一类带有分段常数变量的Lorenz系统的稳定性和分支行为.首先通过计算转化得到Lorenz系统对应的差分系统,利用线性稳定性理论讨论平衡点局部渐近稳定的充要条件.其次选择差分系统三个参数的一个参数为分支参数,利用分支理论研究平衡点处产生Neimark-Sacker分支不变闭曲线的充要条件,并使用分支理论给出判断分支不变闭曲线的稳定性的阈值.最后数值模拟验证了理论分析的正确性.     

一类时滞反应扩散捕食者——食饵模型的Hopf分支分析

针对一类捕食者具有额外食物的时滞反应扩散捕食模型,首先给出了非负平衡点的存在性,然后根据偏泛函微分方程理论,利用系统在平衡点处的特征方程分析了平衡点的稳定性,并给出了Hopf分支存在的充分条件.最后通过数值仿真,直观验证了理论分析的结果.     

具有比率型功能反应捕食-食饵差分系统周期解的存在性

利用重合度理论的延拓定理讨论了具有比率型功能反应的捕食—食饵差分系统的周期解的存在性问题,得到了保证周期解存在的充分条件.     

具有双时滞偏利模型的稳定性分析

主要研究了带有时滞的种群偏利合作模型.首先通过Hurwitz准则得到正平衡点及边界平衡点的局部稳定性条件,然后构造合适的Lyapunov函数给出了正平衡点及边界平衡点的全局稳定性的充分条件.可以看到局部稳定性的充分条件同样也是全局稳定性的充分条件,这一结果补充完善了一些已有的结果.     

一类带有不育控制的离散单种群模型

建立一类不育控制下的害鼠种群的离散模型.首先利用三个Jury条件,得到平衡点的局部渐近稳定性的充分条件.其次利用李雅普诺夫函数和细致分析法分别给出了零平衡点全局稳定及持续生存的充分条件.最后给出了平衡点全局稳定的数值模拟.     

A note on the perfectness concept and the information structures of games

We consider stability of equilibrium points against slight perturbations on the information structures of games from the viewpoint of Selten's concept of perfectness. We give an example in which equilibrium points are not necessarily stable, and provide sufficient conditions for stability. We also point out the difference between our stability and that of Selten's perfect equilibrium point.     

Semistability of switched dynamical systems,Part I: Linear system theory

This paper develops semistability and uniform semistability analysis results for switched linear systems. Semistability is the property whereby the solutions of a dynamical system converge to Lyapunov stable equilibrium points determined by the system’s initial conditions. Since solutions to switched systems are a function of the system’s initial conditions as well as the switching signals, uniformity here refers to the convergence rate of the multiple solutions as the switching signal evolves over a given switching set. The main results of the paper involve sufficient conditions for semistability and uniform semistability using multiple Lyapunov functions and sufficient regularity assumptions on the class of switching signals considered.     

Monodromy and Stability of a Class of Degenerate Planar Critical Points

Necessary and also sufficient monodromy conditions for a large class of degenerate singular points of planar differential systems are given. For these systems, we also find a computable expression of the principal term of the asymptotic expansion of the return map, which gives the stability of the point.     

On the stability of nonautonomous difference equations

In this paper, we obtain new sufficient conditions for the asymptotic stability and instability of equilibrium points of the nonautonomous higher order difference equations by means of weak contractions and weak expansions.     

群体决策问题的一种最优均衡解

本文引进了群体决策问题的一个最优解概念—s~*-最优均衡解,s~*-最优均衡解可以作为群体决策问题的一种解,它的实际意义是为所有的决策者找到一个最优解。我们证明了求解s~*-最优均衡解等价于求解一个相应的单目标优化问题,且在一定条件下s~*-最优均衡解总是存在的。我们也讨论按比例分配的s~*-最优均衡解问题。本文为解决群体决策问题提供了一种新的途径。     

森林病虫害模型的数值模拟

讨论森林病虫害的离散模型.根据森林病虫害传播的特征,针对各分块区域之间已感病树不互相转移的情况,建立差分方程模型;讨论系统的平衡点,并对无病平衡点和地方病平衡点进行稳定性分析,得到地方病平衡点稳定的充分条件;用Matlab进行多种情况的数值模拟,验证了理论结果.     

On the Limit Cycles of Quadratic Differential Systems

In this paper we give the necessary and sufficient conditions for all finite critical points of quadratic differential systems to be weak foci, and solve an open problem proposed by Yanquian Ye. Received January 11, 1999, Revised October 10, 2000, Accepted March 5, 2001     

The Center Conditions and Hopf Cyclicity for a 3D Lotka-Volterra System

The main objective of this paper is not only to find necessary and The main objective of this paper is not only to find necessary and sufficient conditions for the existence of a center on a local center manifold for a three dimensional Lotka-Volterra system, but also to determine the maximum number of limit cycles that can bifurcate from the positive equilibrium as a fine focus. Firstly, the singular point quantities are computed and simplified to obtain necessary conditions for local integrability, and Darboux method is applied to show the sufficiency. Then, the Hopf bifurcation on the center manifold is investigated, from this, the conclusion of at most five small limit cycles generated in the vicinity of the equilibrium is obtained. To the best of our knowledge, this is the first case with five possible limit cycles for the cyclicity of 3D Lotka-Volterra systems.     

Robust stability analysis of static neural network with S-type distributed delays

In this paper, we investigate local robust stability of static neural network (SNN) with S-type distributed delays. We derive some new sufficient conditions for local robust stability of equilibrium points and estimate attracting domains of equilibrium points except isolated equilibrium points. Our results not only show local robust stability of equilibrium points but also allow much broader application for static neural network with or without delays. It is shown that our results are new and improve corresponding results existing in the previous literature.     

Qualitative analysis of Holling type II predator–prey systems with prey refuges and predator restricts

This paper is devoted to investigation of Holling type II predator–prey systems with prey refuges and predator restricts. Using a transformation technique, we change the system into a generalized Liénard system and give sufficient conditions to ensure the global stability of the positive equilibrium and existence and uniqueness of a stable limit cycle. We also find the property of alternation for phase structure of the system.