一类非线性微分系统的反射函数与周期解

采用一种新方法-反射函数法给出了一类非线性微分系统具有满足特定关系式的反射函数和存在周期解的充要条件,得到了此条件下反射函数的具体表达式和周期解的稳定性态.     

广义反射函数的性态与应用

推广了Mironenko的反射函数的概念,给出了广义反射函数的概念并讨论了广义反射函数的性质,应用它研究了微分系统周期解的存在性和稳定性态.作为应用举例,研究了Riccati方程的反射函数.     

二次多项式微分系统的广义反射函数

利用广义反射函数理论,讨论多项式微分系统的广义反射函数的结构形式.并利用所得结论探讨二次多项式微分系统的周期解的几何性质.     

一类三次多项式微分系统的周期解

根据Mironenko的反射函数理论,给出一种利用多项式方程探讨三次多项式微分系统周期解的几何性质的新方法.该文首先研究一类系统具有满足特定关系式的反射函数的结构,由此建立三次多项式微分系统与多项式方程之间的解的对应关系,然后利用此对应关系探讨三次多项式微分系统的周期解的几何性质.     

四维线性微分系统下三角反射矩阵的存在与计算

利用反射函数理论来讨论四阶线性微分系统的下三角反射函数的存在性,并计算出在不同情况下具体的反射矩阵.同时,利用反射矩阵来建立周期微分系统的庞加莱映射,进而该系统周期解的存在稳定性判定定理也相应地建立起来.最后,将以上结果推广应用到了非线性微分系统中.     

n阶线性微分系统的广义反射矩阵与周期解

利用Mironenko的反射函数理论,讨论了n阶线性微分系统的广义反射矩阵并由此得到n阶周期线性系统及与之等价的非线性微分系统的周期解的存在性和稳定性的判定方法.     

多项式微分系统的周期解

给出了多项式微分系统的反射函数第一分量不依赖于第二变量的的充要条件,并应用所得结论研究了周期多项式系统周期解的几何性态.     

非线性微分系统的Poincare映射与周期解

采用一种新方法-反射函数法,建立了非线性非自治微分系统的Poincare映射, 给出了这些微分系统周期解存在及稳定的充要条件．     

微分系统的反射函数与周期解

本文主要介绍了微分系统反射函数与周期解理论的产生与发展动态．论述了一些基本问题，并提出了一些可供研究的新课题。     

二次多项式微分系统的反射函数

本文给出了二次多项式微分系统的反射函数的第一分量不依赖第二分量的充要条件，以及此时第二分量的表示式，及该系统存在周期解的条件。     

THE PERTURBATION OF ALMOST PERIODIC SOLUTION OF ALMOST PERIODIC SYSTEM

By using the exponential dichotomy and the averaging method,a perturbation theoryis established for the almost periodic solutions of an almost differential system.Suppose that the almost periodic differential system(dx)/(dt)=f(x,t) ε~2g(x,t,ε)(1)has an almost periodic solution x=x_0(t,M)for ε=0,where M=(m_1,…,m_k)is theparameter vector.The author discusses the conditions under which(1)has an almostperiodic solution x=x(t,ε)such that x(t,ε)=x_0(t,M)holds uniformly.The results obtained are quite complete.     

Permanence and periodic solutions for an impulsive reaction–diffusion food-chain system with ratio-dependent functional response

An impulsive reaction–diffusion periodic food-chain system with ratio-dependent functional response is investigated in the present paper. Sufficient conditions for the ultimate boundedness and permanence of the food-chain system are established based on the comparison theory of differential equation and upper and lower solution method. By constructing appropriate auxiliary function, the conditions for the existence of a unique globally stable positive periodic solution are also obtained. Some numerical examples are presented to verify our results. A discussion is given in the end of the paper.     

On the Dynamics of an Impulsive Reaction-Diffusion Predator-Prey System with Ratio-Dependent Functional Response

An impulsive reaction-diffusion periodic predator-prey system with ratio-dependent functional response is investigated in the present paper. Sufficient conditions for the ultimate boundedness and permanence of the predator-prey system are established based on the upper and lower solution method and comparison theory of differential equation. By constructing appropriate auxiliary function, the conditions for the existence of a unique globally stable positive periodic solution are also obtained. Some numerical examples are presented to verify our results. A discussion is given in the end of the paper.     

STUDY ON THE THREE-SPECIES ALMOST PERIODIC MODEL WITH THE TYPE II FUNCTIONAL RESPONSE

By using Lyapunov function and differential inequality, sufficient conditions for the existence of global asymptotical stable almost periodic solution of the three-species almost periodic modei with the type II functional response are obtained.     

Dynamics of impulsive reaction–diffusion predator–prey system with Holling type III functional response

An impulsive reaction–diffusion periodic predator–prey system with Holling type III functional response is investigated in the present paper. Sufficient conditions for the ultimate boundedness and permanence of the predator–prey system are established based on the upper and lower solution method and comparison theory of differential equation. By constructing an appropriate auxiliary function, the conditions for the existence of a unique globally stable positive periodic solution are also obtained. Some numerical examples are presented to verify our results. A discussion is given at the end.