CornellMathematics / MAEMAE 6750

Nonlinear Dynamics and Chaos

planned·~150 hours total

Professor

Steven H. Strogatz

Textbook

Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering
Steven H. Strogatz · 3rd · ISBN 9780367026509

Prerequisites

Materials

Strogatz's lectures on nonlinear dynamics, the canonical undergraduate-into-graduate course on the subject. Pairs perfectly with his textbook — the book is one of the best-written maths textbooks in print. Twenty-five lectures available on YouTube.

Covers one-dimensional flows, bifurcations, two-dimensional flows, limit cycles, chaos, fractals, and strange attractors. Apply once differential equations and linear algebra are solid.

Syllabus

Week 1
Introduction to dynamics; flows on the line
Week 2
Bifurcations; saddle-node, transcritical, pitchfork
Week 3
Flows on the circle
Week 4
Two-dimensional flows; linear systems
Week 5
Phase plane
Week 6
Limit cycles; ruling out closed orbits
Week 7
Bifurcations revisited; Hopf bifurcation
Week 8
Chaos in maps; one-dimensional maps
Week 9
Lorenz equations; strange attractors
Week 10
Fractals
Week 11
Period doubling; route to chaos
Week 12
Renormalisation; universality