Phase portraits of ODE systems and vector fields
Click — trajectory from a point. Brush — hold LMB and drag. Wheel — zoom. Axes x and y are phase. Arrows show the vector (ẋ, ẏ), length is speed.
Axes x and y are phase. Arrows show the vector (ẋ, ẏ); length is speed.
Quick reference
An autonomous planar system:
\[ \begin{cases} \dot{x} = P(x,y) \\ \dot{y} = Q(x,y) \end{cases} \]A point with \(P=Q=0\) is an equilibrium. Its type follows from the Jacobian eigenvalues.
Lotka–Volterra produces population oscillations; van der Pol produces a stable limit cycle.
Plot a dynamical-system phase portrait online
ODEPLOT draws the vector field of \(\dot x = P\), \(\dot y = Q\) with speed arrows.
Click the canvas for an integral curve. Examples include Lotka–Volterra, van der Pol, and linear nodes, foci, and saddles. Export PNG.
What you can do on this page
On this page you can draw a phase portrait online, expand the canvas to full screen, animate system parameters and a stream of points on the phase plane, zoom with the mouse wheel, and save a PNG.