一类食饵具常数存放率的Kolmogorov生态系统

本文利用定性分析方法,研究了一类食饵具有常数存放率的Kolmogorov生态系统,讨论了系统平衡点的相对位置和性态,可行平衡点的全局稳定性,给出了一组解的有界性、系统无环性以及极限环的存在唯一性的条件,推广了文[1]和[2]的主要结果.     

一类平面多项式系统极限环的存在唯一性

研究一类平面2n 1次多项式微分系统的极限环问题,利用Hopf分枝理论得到了该系统极限环存在性与稳定性的若干充分条件,利用Cherkas和Zheilevych的唯一性定理得到了极限环唯一性的若干充分条件.     

一类捕食者-食饵系统的全局结构

本文中我们证明了关于一般捕食者-食饵系统不存在闭轨线的定理,即文中定理2.应用这一定理和关于捕食者-食饵系统极限环的存在唯一性定理[1],我们完成了在各种参数条件对一个具体的捕食者-食饵系统模型[2]的研究.     

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。     

一类高次多项式系统的极限环及其对二次系统(Ⅲ)的应用

本文研究多项式系统(?)=-y~α(1-y)~α-δx~α(1-y)~α+lx~(α+1)(1-y)~(α-1)(?)=x~α[(1-y)~α+(ax)~α](α为正奇数)极限环的存在唯一性,完整地分析了该系统的分枝.并将其结果应用于二次系统(Ⅲ)(δ=-m,n=1),彻底解决了极限环的确切个数及分布问题.从而改进了[1—2]的结果.     

负反馈细胞控制系统的极限环的唯一性与稳定性

本文讨论了n维动力系统 x'_1=1/(1 x_n~m)-α_1x_1 (1) x'_j=x_(j-1)-α_jx_j, 2≤j≤n的极限环唯一性和稳定性问题.系统(1)是描述负反馈细胞控制过程(在研究蛋白质合成的遗传调节机制时出现)的数学模型.文[3]证明了系统(1)在有界闭区域T=x\Cg内存在周期轨道.我们用非线性Volterra积分方程理论证明了系统(1)在相空间内的周期轨道是唯一的和稳定的。     

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 .     

Liénard方程极限环的存在唯一性定理

<正> 的极限环的存在唯一性问题[1,2],给出了定理1,此定理的一个推论即已包含了熟知的Lienard定理以及Levinson-Smith[3],Sansone[2],Barbalat[4],余澍祥[5]的存在唯一性定理.作为定理1推论的直接应用,还对方程     

Kolmogorov 捕食者-食饵系统的定性分析

在 Kolmogorov 捕食者-食饵系统(dx)/(dt)=xF(x,y)≡P(x,y),(dy)/(dt)-yG(x,y)≡Q(x,y)(1)中,x 表食饵种群密度,y 表捕食者种群密度.对于系统(1),1936年文[1]得到了著名的 Kolmogorov 定理,后又被文[2]和[13]等推广了.本文得到了系统(1)不存在闭轨线的两个条件,推广了原 Kolmogorov 定理,证明了极限环的唯一性.     

赋值环上的Hermite环猜想北大核心CSCD

本文主要研究赋值环上的Hermite环猜想.根据赋值环V上一元多项式环V[x]的性质,研究并得到V[x]上幺模行向量(a_(1)(x),a_(2)(x),…,a_(n)(x))的一系列关于等价的性质,进而证明了赋值环上的Hermite环猜想成立,即对任意的赋值环V,V[x]都是Hermite环.     

The uniqueness of limit cycles for Liénard system

In monographs [Theory of Limit Cycles, 1984] and [Qualitative Theory of Differential Equations, 1985], eleven propositions by several mathematicians are listed on the uniqueness of limit cycles for equations of type (I), (II), and (III) of the quadratic ordinary differential systems. In this paper, we first point out that all these propositions were not completely proved since the equations under consideration do not satisfy the conditions of the theorems used to guarantee the uniqueness of limit cycles. Then we give a new set of theorems that guarantee the uniqueness of limit cycles for the Liénard systems, which not only can be applied to complete the proof of the propositions mentioned above but generalize many other uniqueness theorems as well. The conditions in these uniqueness theorems, which are independent and were obtained by different methods, can be combined into one improved general theorem that is easy to apply. Thus many of the most frequently used theorems on the uniqueness of limit cycles are corollaries of the results in this paper.     

UNIQUENESS AND DISTRIBUTION OF LIMIT CYCLES FOR BOUNDED QUADRATIC SYSTEM

1 IntroductionAs we know, any given quadratic system which may have limit cycle (LC,fOr abbreviation) can be written in the fOllowing fOrm (see [1] 512)where 6, l, m, n, a, 6 are all real parameters.If all trajectories of a quadratic system remain bounded fOr t 2 0, we saythat the system is bounded, and fOr abbreviation denote by BQS in this paper.The research work for BQS begin with Dickson-Perko [3]. And then, in [4],they made use of the conclusions of [51 to give a detailed classifica…     

Number and Location of Limit Cycles in a Class of Perturbed Polynomial Systems

In this paper,we investigate the number,location and stability of limit cycles in a class of perturbedpolynomial systems with (2n 1) or (2n 2)-degree by constructing detection function and using qualitativeanalysis.We show that there are at most n limit cycles in the perturbed polynomial system,which is similar tothe result of Perko in [8] by using Melnikov method.For n=2,we establish the general conditions dependingon polynomial's coefficients for the bifurcation,location and stability of limit cycles.The bifurcation parametervalue of limit cycles in [5] is also improved by us.When n=3 the sufficient and necessary conditions for theappearance of 3 limit cycles are given.Two numerical examples for the location and stability of limit cycles areused to demonstrate our theoretical results.     

一类异宿环分支问题中极限环的唯一性

在具余维２奇点的四维系统的两参数开折的研究中出现一类三点异宿环的扰动分支,对此异宿环产生极限环的唯一性一直未得到完整的解决,本文圆满地解决了这一问题,并获得了全局分支中极限环的唯一性。     

一类生化系统的数学模型及定性分析

研究了一类非线性生化系统极限环的存在性与唯一稳定性,利用定性分析的方法研究了生化系统轨线的全局结构,给出了极限环存在与稳定的判别条件,改进和推广了已有的结果.     

Uniqueness of limit cycles of the predator-prey system with Beddington-DeAngelis functional response

The goal of this paper is to establish the uniqueness of limit cycles of the predator-prey systems with Beddington-DeAngelis functional response. Through a change of variables, the predator-prey system can be transformed into a better studied Gause-type predator-prey system. As a result, the uniqueness of limit cycles can be solved.     

一类异宿环分支极限环的唯一性

本文研究平面上一类两点或三点异宿环附近极限环的分支,在一简洁条件下证明了异宿环分支极限环的唯一性,并给出了极限环唯一存在的充要条件.作为对三维余维2分支的应用,解决了所出现的两点异宿环产生唯一极限环的问题.     

关于方程 +φ(y)+Ψ(y)η(y)=0的极限环问题

本文研究了(1)的极限环问题,给出了判定其有无闭轨及极限环唯一的若干准则。推广和改进了[1]的结果。     

EXISTENCE AND UNIQUENESS OF LIMIT CYCLE FOR A CLASS OF (2n+1)TH ORDER DIFFERENTIAL SYSTEM

In this paper we consider the problem ofllrmt cycles for thefollowing system【&一y＋6x＋a旷＋a。xy＋a。xy‘＋6xv‘”,(门)!i二 X( 一 by)．Ssstem(1)with k二 b二 0 was studiedin P叩er[1];Ifk 4 0 by transformation:y三 x;V二告;d,二 kdt,system(1)。二。can be trmslated Into the form studiedIn p。per IZ]三 System(1)With口1二 k二 0 W。S Studied ill paper k3]．Ifi System(1;SllPPOSe th。t:(1 ＞2 Is。11 lllteger,k / 0*d 6 / oi(2)。1。2 ＋。5 2 0,this assumption Is the same as that In paper[1];(3)w…