一类三次系统的极限环II

讨论一类三次系统$$\begin{array}{ll}&\dot{x}=-y(1-ax)(1-bx)+\delta x-lx^3,\\1mm]&\dot{y}=x(1-c_1x)(1-c_2x)\end{array}$$的极限环问题.这一系统包括了在$a=c_1,~b=c_2$且$a=-b$或$a=c_1,~b=c_2$或$a=c_1$的限制下的系统.去掉了全部这些限制,得到的极限环存在唯一性定理比以前已得到的相关的定理更具广泛性.

The Limit Cycles for a Class of Cubic Systems II

The limit cycles for the cubic system $$\begin{array}{ll}&\dot{x}=-y(1-ax)(1-bx)+\delta x-lx^3,\\2mm]&\dot{y}=x(1-c_1x)(1-c_2x)\end{array}$$are discussed. With some conditions of parameters, the existence and uniqueness of limit cycle are given. The obtained results generalize the existing ones.