Show that all these phase paths spiral anti-clockwise and

Question

A dynamical system satisfies the equations

x^· = x - y - (x² + y²)x,

y^· = x + y - (x² + y²)y.

Convert this system into polar form and find the polar equations of the phase paths that begin in the domain 0 < r < 1. Show that all these phase paths spiral anti-clockwise and tend to the limit cycle r = 1. Show also that the same is true for phase paths that begin in the domain r > 1. Sketch the phase diagram.