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Phase Portrait Explorer

Vector fields, trajectories, and fixed-point classification

The phase portrait captures all possible behaviors of a 2D continuous-time system dx/dt = f(x,y). Purple arrows show the vector field; click anywhere to trace a trajectory forward and backward in time. Fixed points are classified by the Jacobian's trace and determinant: stable nodes, unstable spirals, saddle points, centers, and limit cycles.

dx/dt = y, dy/dt = -x - mu*y. Classic damped harmonic oscillator.

(0.00, 0.00) stable spiraltr=-0.30 det=1.00
-3-2-10123-3-2-10123xy

Click anywhere on the phase plane to trace a trajectory. Purple arrows show the vector field direction. Colored dots mark fixed points: green = stable, red = unstable, blue = center.

Phase Portrait Explorer -- Systems Thinking Labs · hbar.university