MATH44041/64041: Applied Dynamical Systems

Announcements:


Course Unit Specification: MATH44041/MATH64041
Lecturer: Dr. Yanghong Huang (yanghong.huang@manchester.ac.uk)
Office: Alan Turing 1.108
Office Hour: Thursday 11:00am-12:00pm or appointment or drop by the office (check weekly grid).
Lectures times and locations:

Important Dates: (For a few of you, the Teaching and Learning Office make special arrangements for you to sit your test in a separate location. If this is the case please ignore this general information and go to the location given to you by the Teaching and Learning office.)

Meiss's Book Outline Lecture Notes Tutorial exercies and solutions Scanned notes
Chap 1 ♠ Introduction Part 1 Exercise Sheet 1 (Solution)
Chap 1 ♠ Notation and Basic Concepts Sep 29
Sec 1.2, 4.1, 4.2 ⚬ ODEs: trajectories, phase portrait and flow Oct 02
Sec 4.1 ⚬ Fixed points, perioidic orbits, invariant sets Exercise Sheet 2 (Solution) Oct 06
Sec 3.3 ⚬ Existence and uniqueness
Chap 2,4,5,6 ♠ Linearisation and Equilibria Part 2 Exercise Sheet 3 (Solution) Oct 13
Sec 2.1, 2.3, 2.5 ⚬ Linear systems Oct 20
Sec 6.1, 6.2 ⚬ Planar ODEs
Sec 4.5, 4.6 ⚬ Stability and Lyapunov functions Exercise Sheet 4 (Solution) Oct 27
Sec 5.3, 5.4 ⚬ Nonlinear systems and stable manifold Exercise Sheet 5 (Solution) Nov 06
Sec 1.3 ⚬ Maps: fixed points and periodic orbits Exercise Sheet 6 (Solution) Nov 10
Chap 2, 5, 6 ♠ Periodic Orbits Part 3 Exercise Sheet 7 (Solution)
Sec 5.5 ⚬ Poincare-Bendixson theorem for periodic orbtis Nov 13
Sec 2.8 ⚬ Floquet theory for periodic coefficients Nov 17
Chapter 8 ♠ Bifurcation and Centre Manifold Part 4 Exercise Sheet 8 (Solution) Nov 20
Sec 5.6 ⚬ Centre manifold and its approximation Nov 24
Sec 8.1 ⚬ Extended centre manifold Exercise Sheet 9 (Solution) Nov 27
Sec 8.1, 8.4, 8.6, 8.8 ⚬ Bifurcations Dec 01
Chap 1, 21 ♠ Maps and their bifurcation Part 5 Exercise Sheet 10 (Solution) Dec 04
Sec 1.3 ⚬ Stability of fixed points and periodic orbits Dec 08
Sec 21.1, 21.2, 21.3 ⚬ Bifurcation of maps
Sec 1.3 ⚬ Logistic map and two-dimensional maps Dec 11
*Here blue chapters/sections about maps are referring to Wiggins's book Introduction to applied nonlinear dynamical systems and chaos.
Typos in the online lecture notes (corrected and updated in red):

Midterm, coursework and final exam

"Dynamical" dynamical systems

Below is a list of programs (in matlab)/animations that help you understand the material better.

Recommended Reading:

(for library ebooks, you have to use VPN for off-Campus connection).