一类三次微分系统极限环的存在性和唯一性

The existence and uniqueness of limit cycles for a class of cubic differential systems

研究一类三次微分系统dx/dt=-y(ax2+bx+1)+Dx-lx3 dy/dt=x(ax2+bx+1)在a=0,b≠0与b2=4a两种情形下,讨论该系统极限环的存在性和唯一性.

A class of cubic differential systems is investigated：{dx/dt=-y（ax^2＋bx＋1）＋Dx-lx^3 dy/dt=x（ax^2＋bx＋1）For this system with a=0,b≠0 and b^2=4a,the conditions for the existence and uniqueness of limit cycles are investigated.