The question given is to discuss all bifurcations of the system:
$\dot{x}=x^2+y^2-2$ , $\dot{y}=y-x^2+\alpha$
I know how to discuss bifurcations and what to do after finding the point at which the number of equilibrium points change, however I'm having trouble finding the equilibrium points of the system.
Can I get a little bit of help in finding the equilibrium points of this system?
I know that $\dot{x}=0$ only when $x^2+y^2=2$ which would mean $x=\pm1$ and $y=\pm1$ but that doesn't seem to help when subbing into $\dot{y}$.