摘要
1. Let α, l, m,n, and b be real constants. Regarding the nonlinear autonomous system dx/dt =ax- y+ lx^2+mxy+ny , dy/dt=x+bxy,(1) we have Theorem 1. If α= 0 and if l-b=0 or m^2-An(n+b)≥0, then system (1) possesses no limit cycle in the whole plane. Theorem 2. When α≠0, system (1) may have one unique limit cycle surrounding one of the two critical points O(0, 0) andN ( 0, 1/n) if l-b=0 or l=0. Theorem 3. I fn+b =0 or n=
