一类带有非线性传染率的SEIS传染病模型的定性分析

借助极限理论和Fonda定理,研究了一类既有常数输入率又有因病死亡率的SEIS传染病模型．所考虑模型的传染率是非线性的,并且得到了该模型的基本再生数,当基本再生数小于1时,该模型仅存在唯一的无病平衡点,它是全局渐近稳定的,且疾病最终灭绝．当基本再生数大于1时,该模型除存在不稳定的无病平衡点外,还存在唯一的局部渐近稳定的地方病平衡点,并且疾病一致持续存在．     

Perturbation of a Globally Stable Steady State and Uniform Persistence

In this paper we consider a parametrized family of semi-flows with continuous or discrete time. In the spirit of the global stability result proved by Smith and Waltman (Proc AMS 127:447–453, 1999) we use the upper semi-continuity of a parametrized family of global attractors. Here we investigate the case where the linearized equation of the unperturbed system has a simple dominant eigenvalue 0 in the case of a continuous time system (or 1 in the case of a discrete time system). New difficulties arise since such a system may exhibit a bifurcation. The goal of the paper is to describe the global dynamics of the perturbed system.      

脉冲周期种群动力系统的正周期解

使用Poincare映射和Horn不动点定理对具有脉冲的周期种群生态系统进行研究,得到了脉冲周期种群系统的正周期解存在性,从而为进一步从理论上研究脉冲周期种群动力系统打下基础．     

非自治竞争Lotka-Volterra系统的灭绝性

研究了几个种群非自治Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ竞争系统,给出了竞争的ｎ个种群中任意ｒ个持续生存而ｎ－ｒ个灭绝的一类充分条件。     

一类非线性时滞差分方程解的若干性质

本文研究了一类非线性时滞差分方程解的有界持久性、全局渐近稳定性以及无界解的存在性,所得结果解决及部分解决了文献「４」提出的两个ｏｐｅｎ问题,包含了文献「６」中相应的结果。     

Persistence in a three species Lotka-Volterra nonperiodic predator-prey system

ＩｎｔｒｏｄｕｃｔｉｏｎＴｏｔｈｅａｕｔｈｏｒｓ’ｋｎｏｗｌｅｄｇｅｆｅｗｅｒｌｉｔｅｒａｔｕｒｅ’ｓｃａｎｂｅｆｏｕｎｄｏｎｔｈｅｔｈｒｅｅｓｐｅｃｉｅｓＰｒｅｄａｔｏｒ＿Ｐｒｅｙｓｙｓｔｅｍ .Ｉｎｐａｐｅｒ [1 ] ,ｔｈｅａｕｔｈｏｒｓｏｂｔａｉｎｓｕｆｆｉｃｉｅｎｔｃｏｎｄｉｔｉｏｎｆｏｒｔｈｅｅｘｉｓｔｅｎｃｅｏｆａｇｌｏｂａｌｌｙａｓｙｍｐｔｏｔｉｃａｌｌｙｓｔａｂｌｅｓｔｒｉｃｔｌｙｐｏｓｉｔｉｖｅｐｅｒｉｏｄｉｃｓｏｌｕｔｉｏｎｏｆｔｈｅｆｏｌｌｏｗｉｎｇｔｈｒｅｅｓｐｅｃｉｅｓｐｅ…     

Upper Lipschitz behavior of solutions to perturbed. C1,1 programs

We analyze the local upper Lipschitz behavior of critical points, stationary solutions and local minimizers to parametric C ^1,1 programs. In particular, we derive a characterization of this property for the stationary solution set map without assuming the Mangasarian–Fromovitz CQ. Moreover, conditions which also ensure the persistence of solvability are given, and the special case of linear constraints is handled. The present paper takes pattern from [21] by continuing the approach via contingent derivatives of the Kojima function associated with the given optimization problem. Received: June 10, 1999 / Accepted: November 15, 1999?Published online July 20, 2000     

具有IV类功能反应的非自治捕食系统的持续性和周期解

本文讨论了一类具有HollingIV类功能反应的非自治捕食系统,利用Brouwer不动点定理和构造Liaponov函数的方法,得到该系统永久持续生存和存在唯一全局稳定的周期解的充分条件.     

Attractivity in a Delayed Three—species Ratio—dependent Predator—prey System without Dominating Instantaneous Negative Feedback

A delayed three-species ratio-dependent predator-prey food-chain model without dominating in-stantaneous negative feedback is investigated. It is shown that the system is permanent under some appropriate conditions, and sufficient conditions are derived for the global attractivity of the positive equilibrium of the system.     

环境污染中三维Volterra系统持续生存与绝灭的阈值

本文对环境容量很大且被污染的三种群系统进行了研究，得到了三维Volterra捕食-被捕食系统持续生存与绝灭的阈值．