一类三次系统极限环的唯一性和唯二性

讨论了一类三次系统x=-y(1-βx2)-(a1x a2x2 a3x3),y=b1x b2x2 b3x3的极限环问题.对包含一个奇点或多个奇点的极限环的唯一性和唯二性给出了若干充分条件.

The Uiniqueness and Existence of at Most Two Limit Cycles for a Class of Cubic Systems

This paper gives the sufficient conditions concerning the uniqueness and existence of at most two limit cycles surrounding one or three singular points for a class of cubic systems \begin{eqnarray*}\dot{x}&=&-y(1-\bb x^2)-(a_1x+a_2x^2+a_3x^3),\\\dot{y}&=&b_1x+b_2x^2+b_3x^3.\end{eqnarray*}