Mathematics
Dynamical Systems
Part of Dynamical Systems, level 7. About 53 hours of study across the topics below.
Flows & Maps
- One-Dimensional Systemsfixed points, stability, bifurcations (saddle-node, transcritical, pitchfork)7.5–14 h
- Discrete Maps & Chaoslogistic map, period doubling, chaotic attractors, Lyapunov exponents7.5–14 h
- Two-Dimensional Flowsphase portraits, limit cycles, Poincare-Bendixson theorem7.5–14 h
Advanced Topics
- Bifurcation TheoryHopf bifurcation, normal forms, center manifolds7.5–14 h
- Chaos & Strange AttractorsLorenz system, fractals, sensitive dependence7.5–14 h
- Hamiltonian & Conservative Systemsintegrable systems, KAM theorem intro7.5–14 h
- Dynamical Systems Applicationspopulation models, circuits, lasers, mechanical systems7.5–14 h