How to investigate the stability of the limit cycle of a dynamical system?

Question

Mathematics

A task from the textbook by V.I. Arnold "Ordinary differential equations"
Investigate the stability of the limit cycle r = 1for a system given in polar coordinates by the equations:

d_r/d_t = (r^2 - 1) * (2 * x - 1)
d_phi/d_t = 1

where x = r * Cos(phi)
To be honest, I don’t know how to start it