摘要
研究三次系统具有一条实不变直线和两对共轭复不变直线时的极限环问题，得出在ｍ＝δ，ｌ＝１，２α＋δβ＝０时系统最多有一个极限环，并给出确有一个极限环的条件．还证明当ｍ≠δ，ｌ≠１，ａ０３＝０，ａ３０＝ｂ２０２α＋ｍβ＝０时系统没有极限环．对ａ０１＝０时也证明系统没有极限环．综合以前的工作〔１。
The cubic system with two paris of invariant conjugate imaginary lines, x 2+δxy+y 2=0,δ 2-4<0 and (x-α) 2+m(x-α)+(y-β)+l(y-β) 2=0,m 2-4l< 0,and one real invariant line, y-b =0 has been studied in this paper. Under the conditions of m=δ, l=1 , and 2α+δβ= 0, we prove that there is at most one limit cycle existing in the system. Under the conditions of m≠δ, l≠1 ,2α+mβ= 0 and a 01 =0, we prove that the system has no limit cycle.
出处
《福州大学学报（自然科学版）》
CAS
CSCD
1997年第1期7-12,共6页
Journal of Fuzhou University(Natural Science Edition)
基金
福建省自然科学基金
