摘要
Inthispaperwestudytheexistenceoflimitcycleforcubicsystem（E）3,ofKolmogorovtypewithaconicalgebraictrajectoryF2（x,y）=ax2+2bxy+cy2+dx+ey+f=0Ithasbeenprovedinmyformerpapersthat（E）3doesn’thaveanylimitcycleonthewholeplaneIfb2-ac≠0,Nowweareinvestigatingthecasewhereb2-ac=0.Weprovethesufficientandnecessaryformula（2）or（13）witbwhich（E）3musthaveaparabolictrajectoryF2（x,y）=0.Thentherewillnotbeanylimitcycleonthefullplane.Onthebasisofthis,weconclude:ThecubicsystemofKolmogorovtypewithanon-degeneratedquadraticalgebraictrajectoryonthewholeplanehasnolimitcycle.
出版日期
1989年02月12日（中国期刊网平台首次上网日期，不代表论文的发表时间）
