Phase Portrait Visualizer

Enter a planar autonomous system x' = f(x, y), y' = g(x, y) and get the vector field with nullclines, classified fixed points, and click-to-trace trajectories.

System of equations

Functions: sin, cos, tan, exp, log, sqrt, abs… · constants: pi, e

Examples

Density 22

Window

xmin

xmax

ymin

ymax

Normalize arrow lengthNullclines (x'=0, y'=0)Fixed points

Equilibria (1)

(0.00, 0.00)stable spiral

Trajectories are integrated with RK4 forward and backward from your click. Fixed points are found by Newton's method and classified by the Jacobian's eigenvalues — filled = stable, hollow = unstable, amber = saddle, violet = center.