MAE5790-6 Two dimensional nonlinear systems fixed points

Linearization. Jacobian matrix. Borderline cases. Example: Centers are delicate. Polar coordinates. Example of phase plane analysis: rabbits versus sheep (Lotka-Volterra model of competition in population biology). Stable manifold of a saddle point. Reading: Strogatz, "Nonlinear Dynamics and Chaos", Sections 6.3, 6.4.