一类pitchfork分支的全局相图

Global phase portraits of the key pitchfork bifurcation

本文研究二次微分系统dt/dr=y^2?y?x,dy/dt=x^2?μx?y,其中μ∈R.该系统是刻画pitchfork分支的重要例子.本文给出该系统在Poincare圆盘上的全局相图。

This paper deals with the following quadratic polynomial differential systemdx dt/dr=y^2?y?x,dy/dt=x^2?μx?y,with parameter μ ∈ R, which is the key example for studying the pitchfork bifurcation of a singular point. We classify the global phase portraits in the Poincar′e disc of this system when μ varies.