具有三次曲线解xy2+y=x3的中心对称三次系统极限环的存在性

本文证明了具有三次曲线解ｘｙ²＋ｙ＝ｘ³的中心对称三次系统的极限环存在，而且至少可以存在四个极限环，它们作（２，２）分布．从而纠正了文［１］的结论     

一类具有两个抛物线解的中心对称三次系统存在极限环的条件

本文给出了具有两个抛线解的中心对称三次系统存在在极限环的条件，它可能也是充要条件。     

具三次曲线解的二次系统至多有一个极限环

本文研究具有三次曲线解x^3-x^2-y^2=0的二次系统,证明此类二次系统最多只有一个极限环,进而证明了具有三次的曲线解的二次系统至多有一个极限环。     

具有一类三次曲线解的Kolmogorov三次系统的极限环的存在性

证明了具有三次曲线解y=-x(x-1)2 4/24的Kolmogorov三次系统是有存在极限环可能的.     

三次系统存在一类双纽线分界线环充要条件

给出了中心对称三次系统存在一类双纽线分界线环的充要条件，并举出此系统至少还存在四个极限环的（2．2）分布的例子．还举出了中心对称三次系统至少存在六个极限环作（3.3）分布以及五个极限环，其中一个极限环包围作（2．2）分布的四个极限环的例子．     

中心对称三次系统存在双曲线分界线环的充要条件

本文给出了中心对称三次系统存在双曲线分界线环的充要条件，并证明了此系统还可以至少存在五个极限环。     

具有退化三次曲线解的Hamilton二次系统的Poincare分支

具有退化三次曲线解的Hamilton二次系统,经二次微扰后的Poincare分支,是否存在两个极限环?这是一个长期受到困扰的问题.本文证明了在特定条件下,可以分支出两个极限环.     

以三次曲线为特殊积分的二次系统

本文研究以三次曲线为特殊积分的二次系统:的极限环,得出一类二次系统存在极限环的充要条件。     

一类三次kolmogorov系统的极限环

本研究一类三次kolmogorov系统解的定性行为，给出了系统解的有界性与极限环存在性的充分条件。     

中心对称三次系统的一类双纽线有界周期环域的poincare分支

证明中心对称三次系统的一类双纽线有界周期环域的 poincare分支至少可以出现作对称 (3,3)分布的六个极限环 .     

LIMIT CYCLES OF A QUADRATIC HAMILTONIAN SYSTEM BY CUBIC PERTURBATIONS

In this paper,we are concerned with a cubic near-Hamiltonian system,whose unperturbed system is quadratic and has a symmetric homoclinic loop.By using the method developed in [12],we find that the system can have 4 limit cycles with 3 of them being near the homoclinic loop.Further,we give a condition under which there exist 4 limit cycles.     

A NECESSARY AND SUFFICIENT CONDITION FOR THE COEXISTENCE OF A CLASS OF CUBIC CURVE SEPARATRIX CYCLES AND LIMIT CYCLES TO THE CUBIC SYSTEM

In this paper, we give the necessary and sufficient condition for the coexistence of a class of cubic curve separatrix cycles and limit cycles to the cubic system, and study their topological structures.     

一类三次系统极限环的个数与分布

本文研究一类三次系统的极限环,利用分支理论与定性分析技巧发现这类系统有四个极限环,并给出了他们的分布。     

THE PROBLEM OF LIMIT CYCLES FOR A LIENARD TYPE CUBIC SYSTEM

The purpose of this paper is to study a general Lienard type cubic system with one antisaddle and two saddles. We give some results of the existence and uniqueness of limit cycles as well as the evolution of limit cycles around the antisaddle for system (2) in the following when parameter a1 changes.     

一类三次系统的极限环

本文讨论了一类三次系统 x=-y(1-αx~2)+δx-ιx~3,y=x(1-βx~2)和 x=-y(1-ax)(1-bx)+δx-ιx~3,y=x(1-cx)(1-bx)的极限环问题。     

GLOBAL BIFURCATIONS OF LIMIT CYCLES FOR A CUBIC SYSTEM

1MainResultsConsiderthecubicsystemwheree>Oissmall,parametersa=(a,,a,)EDCR2withDboundedandcl)cz)bl?bzareconstants.LetWesupposep'(y)2ofory/oorequivalentlyoscf53c2.(1.3)Assumethatg(x)hasonlysimplezeroswith6152/o.Withoutlossofgene-ralitywecansuppose610,5z<0(onecenterandtwosaddles);(3)5l-46z<0,bz>0(twocentersandonesaddle),Inthispaperweonlyconsiderthefirsttwocases.Obviously,(1'1).=ohasafamily0fperiodicorbitswhe…     

BIFURCATIONS OF A CUBIC SYSTEM PERTURBED BY DEGREE FIVE

In this article, using multi-parameter perturbation theory and qualitative analysis, the authors studied a kind of cubic system perturbed by degree five and ob-tained the system that can have 17 limit cycles giving their two kinds of distributions (see Fig.5).     

QUALITATIVE STUDY FOR A CUBIC SYSTEM

This article analyses a non-Lienard type planar cubic system, and a complete qualitative analysis is given for the system, especially the conclusions for the non-existence, existence and uniqueness of limit cycles are obtained.     

THE UNIQUENESS OF LIMIT CYCLE AND THE STRUCTURE OF CRITICAL POINT AT INFINITY FOR A CLASS OF CUBIC SYSTEM

A class of cubic system, which is an accompany system of a quadratic differential one, is studied. It is proved that the system has at most one limit cycle, and the critical point at infinity is a higher order one. The structure and algebraic character of the critical point at infinity are obtained.