食饵有常数放养率的广义Rosenzweig-Macarthur系统

本文运用 Liapunov第二方法 ,研究了食饵有常数放养率的广义 Rosenzweig-Macarthur系统x=f ( x) -yφ( x) +H ,y=h( y) [-e+Kφ( x) ]唯一正平衡点的稳定性 .并利用 Poincare-Bendixon环域定理及张芷芬唯一性定理 ,论证了在 R+ 2 ={( x,y)∶x>0 ,y>0 }内极限环的存在唯一性及其稳定性 .     

一类多种群猎物-捕食者生态系统的稳定性

S.B.Hsu 与 S.P.Hubbell 在[1]中研究了有两个猎物、两个捕食者的 MacArther模型,对系统的平衡点在大范围的稳定性态作了细致的论证,得出了很多好的结果,但文[1]对系统存在正平衡点时的稳定性没有深入研究.本文应用 Liapunov 第二方法给出了系统在正平衡点全局稳定的充分条件,并把结果推广到有 n 个猎物,n 个捕食者的情形.     

食饵带疾病的捕食模型的全局稳定性

本文研究了一类三维生态传染病模型的正解性和边界性,并分析了系统平衡点的局部稳定性。利用一种新的几何方法,获得了内平衡点的全稳定性,推广了Li和Muldowney[1]提出的这种方法的应用,这种方法避免了寻找Lyapunov的困难。     

食饵带疾病的捕食模型的全局稳定性（英文）

本文研究了一类三维生态传染病模型的正解性和边界性,并分析了系统平衡点的局部稳定性.利用一种新的几何方法,获得了内平衡点的全稳定性,推广了Li和Muldowney[1]提出的这种方法的应用,这种方法避免了寻找Lyapunov的困难.     

一类微生物连续培养竞争系统的定性分析

研究一类微生物连续培养竞争系统的解的结构,分析了平衡点的稳定性及平衡点附近极限环存在唯一性,证明了该系统存在正向不变集.     

一类具有二阶细焦点的二次系统

文[2]已经证明,具有三阶细焦点的二次系统(叶彦谦形式)当n=0时不存在极限环。本文继续运用文[2]的方法,得到了具有二阶细焦点的二次系统当n=0时在二阶细焦点外围存在极限环的条件和不存在极限环的条件,同时证明这种系统在其他奇点外围不存在极限环。     

一类基于比率的捕食-食饵系统的全局稳定性分析

研究一类基于比率和具第Ⅲ类功能性反应的捕食-食饵系统．通过分析正平衡点的局部稳定性给出了系统正平衡点全局渐近稳定以及系统存在极限环的条件．运用Hopf分支理论讨论了当正平衡点是非双曲型时的情形．     

具有励磁控制的电力系统的稳定性和分岔分析

本文根据[1]所提供的带有励磁控制的发电机电力系统,对该系统的平衡点的局部稳定性和分岔进行了定性分析,当0Vs2(Xd-X'd)/2XdΣ'XdΣ且控制量uf>Efdsc ufc-Efds时,系统存在两类平衡点,其中一类是不稳定的平衡点,而另一类总是稳定的平衡点.Efds uf=Efdsc ufc是鞍结点分岔值,相应于电力系统崩溃.当Efds uf相似文献   

带有积分条件的泛函微分方程的稳定性分析

本文讨论了下列泛函微分方程: 这里T>0,T_1≥0。令Q=bf(a)/c。若Q≤1,则上述方程有唯一平衡点且全局稳定。若Q>1,则上述方程的正平衡点渐近稳定,另一平衡点不稳定。所采用的证明方法是构成Lyapunov泛函和利用广义持征方程,与[2]、[3]不同.当f(y)=y即可得K.L.cooke[3]的结论.当T=T_1=O,f(y)=y即可得[2]的讨论。     

一个至少具有六个极限环的三次微分系统

关于平面三次微分系统的极限环的个数问题,文献[1]、[2]分别得到了在一个奇点的邻域内产生五个环的结果。本文给出了一个至少具有六个极限环的具体例子,从而说明三次微分系统极限环的最大个数不小于六。 考虑系统     

一类具有不同感染率的SIR模型的稳定性分析

建立了一类具有不同感染率且出生和死亡具有密度制约的SIR传染病模型,应用极限系统理论以及Liapunov稳定性定理得到该系统平衡点的稳定性.     

Quasi-separatrix layers and three-dimensional reconnection diagnostics for line-tied tearing modes

In three-dimensional magnetic configurations for a plasma in which no closed field line or magnetic null exists, no magnetic reconnection can occur, by the strictest definition of reconnection. A finitely long pinch with line-tied boundary conditions, in which all the magnetic field lines start at one end of the system and proceed to the opposite end, is an example of such a system. Nevertheless, for a long system of this type, the physical behavior in resistive magnetohydrodynamics (MHD) essentially involves reconnection. This has been explained in terms comparing the geometric and tearing widths [1] and [2]. The concept of a quasi-separatrix layer [3] and [4] was developed for such systems. In this paper we study a model for a line-tied system in which the corresponding periodic system has an unstable tearing mode. We analyze this system in terms of two magnetic field line diagnostics, the squashing factor [5], [6] and [7] and the electrostatic potential difference [8] and [9] which has been used in kinematic reconnection studies. We discuss the physical and geometric significance of these two diagnostics and compare them in the context of discerning tearing-like (reconnection-like) behavior in line-tied modes.     

Hamilton体系与辛正交系的完备性*

本文定义了一个Banach空间ZH,并证明了一类Hamilton体系的本征函数系(辛正交系)在ZH空间中具有完备性.还证明了如下结论ZH空间能连续嵌入到L₂[0,1]×L₂[0,1]但ZH≠L₂[0,1]×L₂[0,1].     

SOME REMARKS ON THE NULL CONDITION FOR NONLINEAR ELASTODYNAMIC SYSTEM

The author derives the same null condition as in[1]for the nonlinear elastodynamic systemin a simpler way and proves the equivalence of the null conditions introduced in[1]and[7]respectively.     

Abstracts to forthcoming papers

There already exist a fairly complete theroy for the problem of estimation and stochastic optimal control for linear distribution parameter systems, with Gaussian or non-Gaussian noise disturbance. In [8] and [12] generalizations of the familiar finite dimensional results of the kalman-bucy filter and the separtion principle are obtained using an abstract input-output Hilbert space representation for the system. However , in [8] and [12] all the input-operators are assumed to be bounded and so it does not cover the important pratical cases of control and noise on submanifolds of the spatial domain or point observations. Here we introduce unbounded system operators in the abstract iput-output Hilbert space reperesentation and thus extend all the results if [8] and [12] to allow for point observations and noise and control on submanifolds including the boundary. the theroy is illustrated by several examples     

Stochastic distributed systems with point observations and boundary control: an abstract theory

There already exists a fairly complete theory for the problems of estimation and stochastic optimal control for linear distributed parameter systems, with Gaussian or non Gaussian noise disturbance. In [8] and [12] generalizations of the familiar finite dimensional results of the Kalman-Bucy filter and the separation principle are obtained using an abstract input-output Hilbert space representation for the system. However, in [8] and [12] all the input operators are assumed to be bounded and so it does not cover the important practical cases of control and noise on submanifolds of the spatial domain or point observations. Here we introduce unbounded system operators in the abstract input-output Hilbert space representation and thus extend all the results of [8] and [12] to allow for point observations and noise and control on submanifolds including the boundary. The theory is illustrated by several examples.     

An existence theorem for systems of linear equations

Given is a constructive proof of the following theorem: A system of linear equations has a [nonnegative] solution if and only if each system constructed by replacing each equation by one of the two associated inequalities has a [nonnegative] solution.     

CONVERGENCE OF SOLUTIONS OF CERTAIN SYSTEM OF THIRD ORDER NON-LINEAR ORDINARY DIFFERENTIAL EQUATIONS

The object of this paper is to give an n-dimensional analogue of a convergence result of Tejumola [8] for some third-order differential equations. The result extends earlier results of Afuwape [1] and Ezeilo [4] to some system of third-order differential equations.     

A Spectral Method for a Class of System of Multi-Dimensional Nonlinear Wave Equations

In [1,2], the problem of three-dimensional soliton of a class of system for three-dimensional nonlinear wave equations was investigated, and the existence and stability of three-dimensional soliton was proved. In [3] the system discusses in [1,2] was generalized and a more general class of system of multi-dimensional nonlinear wave equations were studied. It was proved that the solution of its initial-boundary value problem was well posed under some conditions. This system has been studied by the finite difference method and the finite element method [4,5]. In this paper, we take the trigonometric functions as a basis to derive a spectral method for the system and give a strict error analysis in theory.     

一类三阶非线性微分方程解的不稳定性*

文献[1]讨论了非线性缓变系统的渐近稳定性,文献[2]讨论了三阶变系数线性微分方程解的不稳定性。本文应用文献[1]、[2]的方法讨论一类三阶非线性微分方程解的不稳定性。