一类五次系统赤道环的稳定性与极限环分枝

本文解决了一类五次系统赤道环的稳定性与极限环分枝问题，所得的结论与二次系统的若干结论形 成有趣的对比．     

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。     

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.     

一类三次系统的极限环个数与奇点分支

给出二次系统I的一类相伴系统在奇点O(0,0)的焦点量公式,证明了O至多为2阶细焦点,δlmn=0时系统在O外围至多有一个极限环,从而说明了系统在细焦点外围至多有一个极限环。最后给出了各个奇点的分支情况及几何特征。     

一类五次系统赤道环的稳定性与极限环分枝

本文解决了一类五次系统赤道环的稳定性与极限环分枝问题,所得的结论与二次系统的若干结论形成有趣的对比.     

一类五次系统的赤道极限环问题

本文解决了一类五次系统赤道环的稳定性与极限环分枝问题,所得的结论与三次系统的若干结论形成有趣的对比.     

LIMIT CYCLES FOR A CLASS OF E_3~1 SYSTEMWITH A FINE FOCUS AND A FINE SADDLE

1IntroductionManypracticalproblems,suchasnon--linearvibration,reactionofbiochemistrygandself-oscillatingsystem,etc.canbereducedtotheproblemsonthelimitcyclesofEjsystem.Therefore,thestudyoflimitcyclesforEjsystemhaspracticalsignificances.ThesocalledEdsystemi…     

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.     

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…     

一类平面微分系统极限环的存在唯一性

研究一类平面微分系统的极限环,利用Hopf分支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Л.A.Чepkac和Л.ИЖилевьыч的唯一性定理得到了极限环唯一性的若干充分条件.     

一类Kolmogorov捕食系统的极限环

本文研究Ｋｏｌｍｏｇｒｏｖ的捕食系统ｘ＝ｘ（ａ０＋ａ１ｘ－ａ２ｘ＾２－ψ（ｙ）） ｙ＝ｙ（ｂｘ＾２－ｄ），得到了极限环存在唯一的充要条件，从而推广了前人相关的结果，其中ψ（０）＝０，ψ（ｙ）＞δ＞０，ｙ＞０。     

LIMIT CYCLES FOR A CLASS OF FIFTH-ORDER DIFFERENTIAL EQUATIONS

In this paper, we study a fifth-order differential equation. Using the averaging theory, we investigate the limit cycles of the equation.     

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.     

BOUNDEDNESS OF SOLUTIONS AND EXISTENCEOF LIMIT CYCLES FOR A NONLINEAR SYSTEMOF DIFFERENTIAL EQUATIONS

IntroductionTheautonomousplanarsystemoftheformwasfirststudiedbyLevinsonandSmithintheclassicalpaper[2]astheequivalelltsystellloftheequationofLienardtypeandlateronsomeauthorshavecontributedtotiletheoryofthissystemwithrespecttoqualitativebehaviorofsolutionsll--9].InthepresentpaperwestudyasystemOfaslightlymoregeneraltype,namely,wherethefllnctionsp(y),q(y),g(x)andh(x,y)arecontilluousforallvalueoftheirarguments,and3'resubjecttotheconditionswhichensurethattheexistenceofuniquesolutiontotheinitialvalu…     

一类三次系统极限环的存在唯一性

本文得到三次系统x=-y(1-ax)(1-ax) δx-lx3,y=x(1-ax)(1-bx)极限环的存在性、唯一性及不存在性的完整结果．     

LIMIT CYCLES FOR A CLASS OF DIFFERENTIAL SYSTEM WITH POSITIVE DEFINITE POLYNOMIAL

In this paper we consider a class of differential systems with positive definite polynomial having exactly one and two limit cycles.Such a system is more extensive than paper[1,2].     

一类7次微分自治系统的极限环分支

研究一类平面7次微分系统,通过作两个适当的变换以及焦点量的仔细计算,得出了系统的无穷远点与2个初等焦点能够同时成为广义细焦点的条件,进一步得出在一定条件下该系统能够分支出15个极限环的结论,其中5个大振幅极限环来自无穷远点,10个小振幅极限环来自2个初等焦点.     

ON LIMIT CYCLES FOR A CLASS OF DIFFERENTIAL SYSTEMS WITH POSITIVE DEFINITE POLYNOMIAL

In this paper, the nonexistence, existence and the number of limit cycles for a class of differential systems with positive definite polynomial are considered, and the results obtained generalize and supplement those of [1].