三次Kolmogorov捕食系统的多个稳定极限环_英文_.pdfVIP

18 4 Vol. 18 No. 4 2001 11 JOU RNAL OF ENGINEERING MAT HEMAT ICS Nov. 2001 Article ID 200 1) Multiple Stable Limit Cycles for a Cubic Kolmogorov PreyPredator System 1 2 LU Zhe gyi , HE Bi ( 1In titute of Sy tem Science, Wenzhou Norm al College, Wenzhou 325003; 2Department of M athematic , Sichuan Univer ity, Chengdu 610064) Abstract:A cubic Kolmogorov preypr edator y tem i con tructed and i hown to hav e three mall amplitude limit cycle , among which two ar e table. T hi can erve a an affirmative an wer to a que tion pr o po ed by Coleman( 1982) . T he computer alg ebraic y tem, Maple, i applied to manipulate polynomial in dealing with the y tem. Keywords:Kolmogorov y tem; polynomial ; computer algebraic; table limit cycle Classificatio : A M S( 2000) 92A17 CLC umber: Q14 1 Docume t code: A Con ider the follow ing tw o pecie Kolmog orov y tem , x= xf 1( x , y ) , y= yf 2( x , y ) ( 1) If bothf 1 andf 2 are linear, ( 1) i the wellknown LotkaVolterra y tem and ha no i olated periodic orbit ( limit cycle) [ 1] . A complete analy i for twopecie LotkaVolterra y tem can be found in [ 2] . Whenf 1 andf 2 are quadratic, ome re ult for the exi tence of multiple limit cycle are given, for example , in [ 3, 4] . In [ 4] , tw o limit cy cle are con tructed and one i table and the other i un table. In [ 3] , f 1 and f 2 are factorized to be the product of linear function , re pectively , and the y tem i not the preypredator type. In another a