4.I.7B

Dynamical Systems
Part II, 2005

Find and classify the fixed points of the system

x˙=x(1y)y˙=y+x2.\begin{aligned} &\dot{x}=x(1-y) \\ &\dot{y}=-y+x^{2} . \end{aligned}

Sketch the phase plane.

What is the ω\omega-limit for the point (2,1)(2,-1) ? Which points have (0,0)(0,0) as their ω\omega-limit?