given system of ODE

dx/dt = ax+xy-x^3

dy/dt = b-x^2-y^2

first, show that there is saddle-node bifurcation for b=0, without using the theorem

second, determine the curve in the a-b plane for which there exists a pitchfork bifurcation without using the theorem

third, sketch the full bifurcation set in the a-b plane (including homoclinic bifurcation)

Help plz