LIMIT CYCLES AND INVARIANT PARABOLA IN A KUKLES SYSTEM OF DEGREE THREE  

作　　者：刘振海 E.Sáez I.Szántó 

机构地区：[1]Department of Mathematics,Changsha University of Sciences and Techndogy [2]Departamento de Matemática,Universidad Tcnica Federico Santa Maria,Casilla 110-V,Valparaiso,Chile

出　　处：《Acta Mathematica Scientia》2008年第4期865-869,共5页数学物理学报（B辑英文版）

基　　金：NNSF of China(10671211);NSF of Hunan Province(07JJ3005);USM(120628 and 120627)

摘　　要：In this article,the authors consider a class of Kukles planar polynomial differential system of degree three having an invariant parabola.For this class of second-order differential systems,it is shown that for certain values of the parameters the invariant parabola coexists with a center.For other values it can coexist with one,two or three small amplitude limit cycles which are constructed by Hopf bifurcation.This result gives an answer for the question given in[4],about the existence of limit cycles for such class of system.In this article,the authors consider a class of Kukles planar polynomial differential system of degree three having an invariant parabola.For this class of second-order differential systems,it is shown that for certain values of the parameters the invariant parabola coexists with a center.For other values it can coexist with one,two or three small amplitude limit cycles which are constructed by Hopf bifurcation.This result gives an answer for the question given in[4],about the existence of limit cycles for such class of system.

关 键 词：Kukles system limit cycles invariant algebraic curves 

分 类 号：O175[理学—数学]