一类多项式系统极限环的唯一性与分支

Uniqueness and Bifurcation of Limit Cycles for a Class of Polynomical System

该文讨论的是一类多项式系统:dx/dt=-y+δx^2+lx^2+mxy+ax^3,(dy)/(dt)=x(1+b_1y+b_2y^2+…+b_nx^n)(b_n≠0).求出该系统在O(0,0)的焦点量公式,得出在δma=0时系统至多存在一个极限环的结论.

In this paper, a class of polynomical systems：dx/dt=-y＋δx＋lx2＋mxy＋ax3,dy/dt=x（1＋b1y＋b2y2＋…＋bnxn）is studied. It gives the succesive focal values, and provesthat the system has at most one limit cycle when δma = O.