摘要
本文继[1]研究系统dx/dt=δx-y+mxy-y^2,dy/dt=x+ax^2 (a<0) (1)极限环集中分布问题。在(a,m)参数平面的角域0<m≤-a内找到一条分枝曲线F(a,m)≡(m+2a)/2((m-2a)/2)~2-a=0,当F(a,m)≤0时,系统(1)的极限环是集中分布或不存在。
In this paper, we consider the relative position of limit cycles for the systemdx/dt-y+my-y^2, dy/dt=x+ax^2. (1)WriteF(n, m)≡((m+2a)/2(m-2a)/2)~2-a=0,D={(a, m)|0<m≤-a}, and D=D_1∪D_2,where D_1={(a,m)|0<m≤-a, F(a, m)≤0},D_2≡{(a,m)|0<m≤-a, F(a, m)>0},The main result is as follows:(ⅰ) Under condition (a, m)∈ D_1, if δ=m/2+m^2/4a≡δ_0, then system (1)_δ, has no limit cycles and singular closed trajectory through a saddle point in the whole plane.(ⅱ) Under condition (a, m)∈ D_1, 0<δ≤m, the foci o and R cannot be surrounded by the limit cycles of the system (1) simultaneously.
出处
《华中师范大学学报（自然科学版）》
CAS
CSCD
1989年第1期15-18,共4页
Journal of Central China Normal University：Natural Sciences
