Undergraduate Course: Dynamical Systems (MATH11027)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 11 (Year 4 Undergraduate)
||Availability||Available to all students
|Summary||Course for final year students in Honours programmes in Mathematics.
Concepts of continuous and discrete dynamical systems. Orbits, fixed points and periodic orbits. Poincare maps. Classification of fixed points for linear discrete systems. Fixed points in nonlinear systems: stable and unstable manifolds. Bifurcation theory for one and two dimensional systems: saddle-node, flip and Hopf bifurcations. Logistic map: period-doubling cascade and chaos. Chaotic attractors and fractals.
Information for Visiting Students
Course Delivery Information
|Not being delivered|
| 1. Ability to identify and classify of fixed points of discrete systems.
2. Ability to construct of stable and unstable manifolds for nonlinear systems.
3. Ability to calculate an appropriate normal form for nonlinear systems and thereby deduce the stability of fixed points.
4. Ability to characterise saddle-node, flip and Hopf bifurcations.
5. Appreciation of the period-doubling cascade and the notion of chaotic systems.
6. Ability to calculate Liapunov exponents.
7. Familiarity with attractors and basins of attraction.
|Course organiser||Dr Jacques Vanneste
Tel: (0131 6)50 6483
|Course secretary||Mrs Alison Fairgrieve
Tel: (0131 6)50 5045