AJSesinando
Phase Plane Analysis
Plotting trajectories in the (x, y) state plane classifies equilibria by the eigenvalues of the linearization: real same-sign eigenvalues give nodes, opposite signs give saddles, and complex eigenvalues give spirals or centers, with the real part deciding stability. For nonlinear systems the Jacobian at each equilibrium supplies the linearization, valid except in the borderline center/zero-eigenvalue cases.