THE APPLICATION OF PERTURBATION METHODS TO ECOLOGY

In this paper,we study the application of perturbation methods to ecology.We obtainthe asymptotic solution of an ecolgical differential equation.     

两类两种群动力学方程的稳定性分析

本文研究两种群动力学方程平衡点的稳定性.讨论两个捕食者-食饵-领地模型,模型用1微分方程描述,模型2用积分微分方程描述.得出平衡点稳定的条件.所得结果指出可实现总体的种群稳定而不管局部的绝灭.     

两个含人口迁移的流行病模型

本文研究含人口迁移的流行病学模型,把k-M模型推广到部分移除的情形和非常数传染力情形,并讨论人口迁移对传染病的流行特征的影响.     

一类含时滞的非线性传染病模型的定性分析和渐近分析

本文研究一个钩虫传染病模型,得到一类含时滞的非线性微分方程组,讨论解的稳定性,并应用摄动方法求渐近解,论证它的渐近性     

Stability analysis for two kinds of equations in two-species population dynamics

In this paper we study the stability for equilibrium points of equations in two-population dynamics.We discuss two predator-prey-patch models.Model1 is described by a differential equation.Model2 is described by an integral differential equation.We obtain the conditions for the stability of their equilibrium points.The results show that the overall population stability despite local extinction is realizable.     

摄动方法在生态学中的应用

本文研究摄动方法在生态学中的应用,得到一个生态方程的渐近解。     

The application of perturbation methods to ecology

In this paper, we study the application of perturbation methods to ecology. We obtain the asymptotic solution of an ecological differential equation.     

放牧系统动态平衡的产生和消除

近年来生物数学研究的课题之一是各种生态系统动态平衡产生的条件,在一定条件下建立生态系统的微分方程模型,研究在什么条件下产生周期解.在实际应用中碰到这样的情形,如果生态系统存在动态平衡,而且振动幅度较大,那么生物种群数在一个周期内产生急剧的变化,在某些时刻下降到很低,甚至可能使某种生物绝灭.因此需要研究在不改变生态系统本身参数的条件下消除这种周期现象的方法.本文研究一类放牧系统,给出对应的数学模型存在周期解的条件,并通过引入适当的人为捕猎来消除动态平衡.     

一类流行病模型的分析

本文研究一类流行病模型。把Kermack-Mckendrick模型加以推广,讨论平衡点的稳定性,得到流行的条件。     

Effects of hunting on the stability of ecosystems

In this present paper, we examine the effects of hunting on the stability of prey-predator systems and grazing systems. The theory of stability and singular perturbationmethod are applied for analysing.