一类二次等时微分系统在不连续二次多项式扰动下的极限环分支

Limit Cycles for Perturbing Quadratic Isochronous Center Inside Discontinuous Quadratic Polynomial Differential System

该文研究了二次等时微分系统x=-y-4/3x^2,y=x-16/3 xy在不连续二次多项式扰动下的极限环分支问题.结果表明该系统从原点的周期环域最多可以分支出4个极限环.并且,这个上界是可以达到的.

In this paper,we bound the number of limit cycles which bifurcate from the period annulus of a class of quadratic isochronous center x=-y-4/3x2,y=x-16/3xy,when perturbed inside the class of all discontinuous quadratic polynomial differential systems.Our results show that there are at most 4 limit cycles bifurcating from this system.Moreover,this bound is sharp.