Dynamics and chaos

Linear differential equations

Linear flows

Explore linear systems through animated trajectories, vector fields, and the trace–determinant plane.

Open linear flows →

Forced oscillations

Forced oscillators

Explore harmonic and Duffing oscillators through motion, phase portraits, resonance, and nonlinear spring potentials.

Open forced oscillator →

Nearby trajectories

Variational equations

Follow a moving variational vector and compare its prediction with nearby solutions, from linear flows to chaotic systems.

Open variational equations →

Changing a parameter

Bifurcations in 2D

Move through a family of nonlinear systems and watch nullclines, equilibria, and saddle connections change at critical parameter values.

Open 2D bifurcations →