摘要
本文首先运用Hopf分支理论 ,论证了三次 微分系统 (1 ) ;对充分小的 μ >0 ,在奇点0 (0 ,0 )附近至少存在一个稳定的极限环 然后运用闭轨分支出极限环理论 ,论证了三次微分系统 (2 ) ;对充分小的｜μ｜ ,在闭曲线x2 +x42 +y2 =740 - 1 01 0 附近存在唯一极限环 μ>0是稳定环 ;μ<0是不稳定环 同理论证了三次微分系统 (3) 对充分小的｜μ｜ ,分别在闭曲线x2+x42 +y2 =1 31 - 2 76130 0 和x2 +x42 +y2 =1 31 +2 76130 0 附近存在复合极限环г0 和г1 μ >0 ,г0 是稳定环 ;μ<0 ,г0 是不稳定环 而 μ>0 ,г1 是不稳定环 ;μ<0 ,г1
In the paper We usod Hopl branch theory to prove that three order differential system(1);has a stable Limit ring at 0(0,0) when n tonds toward zero,Send,We use elosed locus branch limit ring thoory to prove that system(2);has only limit ring which is stablo when μ>0 and not stable μ<o at x 2+x 4/2+y 2=740-1010 and that system(3).has limit rings г 0,г 1 at x 2+x 4/2+y 2=(131-2761)/300 and x 2+x 4/2+y 2=(131+2761/300 reapectively whon μ tends toward zero.г 0 is г 1 stable when μ>0 and not stable μ<0,г 1 is not stable when μ>0 and stable μ<0.
出处
《松辽学刊（自然科学版）》
1998年第4期23-26,共4页
Songliao Journal (Natural Science Edition)
