- Course policies and general information:
- Assignments and solutions
- Tests and solutions
- Lecture materials
- Chapter 1 lecture slides: Introductory ideas
- Chapter 2 example: Xppaut input file for the exciplex mechanism
- Section 3.1: Linear stability analysis
- Section 3.2: Lyapunov functions
- Sections 4.2, 4.3, 5.1 and 5.2: Saddle-node and transcritical bifurcations
- Lecture slides
- Xppaut for in-class example: photoactivated enzyme
- Input file for bifurcation analysis
- Input files for visualizing hysteresis: ODE file and animation script

- Notes for in-class example: SI model of an infectious disease

- Section 4.4: Andronov-Hopf bifurcations
- Sections 4.5 and 5.3: Period-doubling bifurcations and chaos
- Chapter 6: Invariant manifolds
- Lecture slides
- Notes for in-class example: centre manifold of the exciplex mechanism
- Interlude: the Lotka-Volterra model
- Xppaut input file for the Lotka-Volterra model
- Maple worksheet for the HIV model of section 6.5.2. Because there are few comments in this worksheet, I strongly suggest that you read this worksheet alongside the explanations in the textbook.

- Chapter 7: Singular perturbation theory
- Lecture slides: Introduction to singular perturbation theory and Tikhonov's theorem
- Notes for in-class example: scaling and Tikhonov's theorem applied to an ozone decomposition model
- Lecture slides: inner and outer solutions of singularly perturbed equations
- Notes for in-class example: inner and outer solutions
- Maple worksheet: global approximation to the time evolution in the ozone decomposition model
- Notes for in-class example: geometric singular perturbation theory
- Maple worksheet: geometric singular perturbation theory calculation of the slow manifold

- Chapter 8: Hamiltonian systems
- Chapter 10 lecture slides: Maps and differential equations
- Chapter 11: stability and bifurcations in maps
- Lecture slides: Fixed points, stability and bifurcations
- Maple worksheet: analysis of the logistic map
- Maple worksheet: sensitive dependence on initial conditions
- Lecture slides: sensitive dependence on initial conditions
- Matlab/Octave code to compute the Lyapunov exponent of the logistic map, function defining the logistic map and function defining the derivative of the map

- Lab materials
- Useful stuff: