MTH744 |
Dynamical Systems |
Lecturer: Thomas Prellberg | Semester 1, 2012/2013 |
Module information
Textbook
Lecture Notes
lecture | date | sections | content |
---|---|---|---|
1 | 27/9 | 1 | Introduction |
2 | 27/9 | 2.1 | One-dimensional ODEs |
27/9 | No Exercise class | ||
3 | 4/10 | 2.2-2.3 | Fixed Points and Stability |
4 | 4/10 | 2.4 | Linear Stability Analysis |
4/10 | Exercise class: 2.2.8,9; 2.3.1,3; 2.4.7,8 | ||
5 | 11/10 | 2.5-2.7 | Existence and Uniqueness; Impossibility of Oscillations; Potentials |
6 | 11/10 | 3.1 | Saddle-Node Bifurcations |
11/10 | Exercise class: 2.6.2; 2.7.7; 3.1.2 | ||
7 | 18/10 | 3.2 | Transcritical Bifurcation |
8 | 18/10 | 3.4 | Pitchfork Bifurcation |
18/10 | Exercise class: 3.1.5; 3.2.4,6; Sample Exam Question 1 | ||
9 | 25/10 | 3.6 | Imperfect Bifurcations |
10 | 25/10 | 4.1-4.3 | Flows on the circle |
25/10 | Exercise class: 3.4.2,16; 3.5.8; 3.6.2 | ||
11 | 1/11 | 4.4 | Flows on the circle |
12 | 1/11 | 5.1 | Two-dimensional flows |
1/11 | Exercise class: 4.3.7; 4.4.4; 5.1.2,9 | ||
Reading Week: Insect Outbreak (3.7) and Fireflies (4.5) | |||
13 | 15/11 | 5.1 | Linear flows |
14 | 15/11 | 5.2 | Classification of Linear Flows |
15/11 | Exercise class: any of 5.2.3-10; 5.1.12 | ||
15 | 29/11 | 6.2-6.3 | Phase plane |
16 | 29/11 | 6.4 | Lotka-Volterra model |
29/11 | Exercise class: 6.1.3, 6.2.2; 6.3.4,16 | ||
17 | 6/12 | 6.5-6.6 | Conservative systems; Reversible Systems |
18 | 6/12 | 7.1 | Limit cycles |
6/12 | Exercise class: 6.5.2; 6.6.3; 7.1.3 | ||
19 | 13/12 | 7.2 | Ruling out closed orbits |
20 | 13/12 | 7.3 | Poincare-Bendixson Theorem |
13/12 | Exercise class: 7.2.6,10; 7.3.1 |
Thomas Prellberg
September 2012