MTH744 |
Dynamical Systems |
Lecturer: Thomas Prellberg | Semester 1, 2011/2012 |
Module information
Textbook
Lecture Notes
lecture | date | sections | content |
---|---|---|---|
1 | 29/9 | 1 | Introduction |
2 | 29/9 | 2.1 | One-dimensional ODEs |
29/9 | No Exercise class | ||
3 | 6/10 | 2.2-2.3 | Fixed Points and Stability |
4 | 6/10 | 2.4-2.5 | Linear Stability Analysis; Existence and Uniqueness |
6/10 | Exercise class: 2.2.8,9; 2.3.1-4; 2.4.7,8 | ||
5 | 13/10 | 2.6-2.7 | Impossibility of Oscillations; Potentials |
6 | 13/10 | 3.1 | Saddle-Node Bifurcations |
13/10 | Exercise class: 2.7.7; 3.1.2,3,5 | ||
7 | 20/10 | 3.2 | Transcritical Bifurcation |
8 | 20/10 | 3.4 | Pitchfork Bifurcation |
20/10 | Exercise class: 3.2.4,6; 3.4.2,16 | ||
9 | 27/10 | 3.6 | Imperfect Bifurcations |
10 | 27/10 | 4.1-4.3 | Flows on the circle |
27/10 | Exercise class: 3.5.8; 3.6.2; 4.3.7 | ||
11 | 3/11 | 4.4 | Flows on the circle |
12 | 3/11 | 5.1 | Two-dimensional linear flows |
3/11 | Exercise class: 4.4.4; 5.1.2,9 | ||
Reading Week: Insect Outbreak (3.7) and Fireflies (4.5) | |||
13 | 17/11 | 5.2 | Linear flows |
14 | 17/11 | 6.1 | Phase plane |
17/11 | Exercise class: 5.1.12; 6.1.3,8 | ||
15 | 24/11 | 6.2-6.3 | Phase plane (continued) |
16 | 24/11 | 6.4 | Lotka-Volterra model |
24/11 | Exercise class: 6.2.2; 6.3.4,16 | ||
17 | 1/12 | 6.5-6.6 | Conservative systems; Reversible Systems |
18 | 1/12 | 7.1 | Limit cycles |
1/12 | Exercise class: 6.5.2; 6.6.3; 7.1.3 | ||
19 | 8/12 | 7.2 | Ruling out closed orbits |
20 | 8/12 | 7.3 | Poincare-Bendixson Theorem |
8/12 | Exercise class: 7.2.6,10; 7.3.1 | ||
21 | 15/12 | 9 | The Lorenz equations and chaos |
22 | 15/12 | 9 | Chaos and strange attractors |
Thomas Prellberg
September 2011