具有两个相切圆解的三次系统的极限环

Limit Cycles of a Cubic System with Two Tangent Circle Solutions

Paper 1] gave out the necessary and sufficient codition for the existence of two separated circle solutions as its limit cycles in a cubic system, and then proved that there is no other limit cycles when the two circle solutions become limit cycles. In fact, in a cubic system there exists no other limit cycle, no matter whether the two circle solutions are limit cycles or not. In this paper, we prove that other limit cycle may exist for the cubic system with two tangent circle solutions.