Nullclines & Phase Portrait

Phase Plane (click to add trajectory)

Nullclines: The x-nullcline (green) is where dx/dt=0; the y-nullcline (magenta) is where dy/dt=0. Their intersections are fixed points of the flow. The vector field (arrows) shows the direction of motion everywhere. Stability is determined by the Jacobian eigenvalues at each fixed point: negative real parts → stable, positive → unstable, imaginary → center/oscillation. The limit cycle of the Van der Pol oscillator emerges from a Hopf bifurcation at μ=0.