Dynamical Systems Lab

From fixed points and bifurcations to Hopf oscillations, strange attractors, and the universal route to chaos — nine lessons covering the mathematics and physics of nonlinear dynamical systems, each with detailed derivations and a live interactive demo.

Labs

1 - Fixed Points and Stability Apr 2026
2 - Bifurcations in 1D Apr 2026
3 - 2D Phase Portraits Apr 2026
4 - Limit Cycles and the Van der Pol Oscillator Apr 2026
5 - The Lorenz System and Chaos Apr 2026
6 - Lyapunov Exponents Apr 2026
7 - Strange Attractors and Fractals Apr 2026
8 - Hopf Bifurcation Apr 2026
9 - Routes to Chaos Apr 2026

Live Demos

→ Phase Line 1D flows & fixed points ⑂ Bifurcations Saddle-node · pitchfork · transcritical ↺ Phase Portrait 2D flows & nullclines ∿ Van der Pol Limit cycles 🦋 Lorenz Attractor Chaos & butterfly effect λ Lyapunov Exponent Quantifying chaos ∵ Hénon Map Strange attractor & fractals ⥁ Hopf Bifurcation Equilibrium → limit cycle ⟳ Logistic Map Period doubling · Feigenbaum