Vector fields, nullclines, and trajectories — click to launch trajectories
DYNAMICAL SYSTEM
dx/dt = y dy/dt = −sin(x)
DISPLAY
16
SYSTEM PARAMS
LEGEND
─ dx/dt nullcline
─ dy/dt nullcline
● Unstable fixed pt
● Stable fixed pt
● Center/saddle
Click canvas → launch trajectory
About: The phase plane displays the state space of a 2D dynamical system (dx/dt=f(x,y), dy/dt=g(x,y)). Nullclines are curves where one derivative is zero — their intersections are fixed points (equilibria). Fixed point stability is determined by the Jacobian eigenvalues: negative real parts → stable node/spiral, positive → unstable, complex → spiral/center, real with opposite signs → saddle. The Van der Pol oscillator (μ=0) has a stable limit cycle. Lotka-Volterra models predator-prey cycles: closed orbits around the coexistence equilibrium. The Duffing oscillator has multiple wells and can exhibit chaos with forcing.