Nonlinear Dynamics and Chaos

Academic (University) preparation with worked examples, written practice and independent learning assessments.

Independent university-level study of Nonlinear Dynamics and Chaos. This original curriculum draws on public academic subject descriptions; it is not an official faculty syllabus, university credit, accreditation or an Ivy League qualification. Topics covered: Phase portraits; Fixed points; Linearization; Local stability. One-dimensional flows; Potential functions; Bifurcations; Hysteresis. Planar systems; Nullclines; Limit cycles; Poincare-Bendixson theorem. Hopf bifurcation; Normal forms; Center manifolds; Oscillatory instabilities. Discrete maps; Period doubling; Logistic map; Lyapunov exponents. Strange attractors; Lorenz equations; Fractals; Sensitive dependence. Hamiltonian dynamics; Invariant tori; Resonance; Chaotic transport. Time-series reconstruction; Numerical pitfalls; Parameter exploration; Nonlinear modeling project. Projects use safe simulations, public datasets or textual analysis; specialist subject review is required. Includes lessons, supplementary YouTube tutorials, practical exercises, quizzes and free/paid practice tests. Erudex is independent, not affiliated with the source institution or awarding body. Its 80% learning checks are not official grades or university credit. Content requires qualified subject review before use as a complete teaching programme.