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.
Presets (examples with parameters)
Axes x and y are phase. Arrows show the vector (ẋ, ẏ); length is speed.
System
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.