Dynamical Systems (U01875)

? Credit Points : 10 ? SCQF Level : 11 ? Acronym : MAT-4-DSy

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.

Entry Requirements

? Pre-requisites : MAT-3-CVD

Variants

? This course has variants for part year visiting students, as follows

Dynamical Systems (VS1) (Semester 1 (Blocks 1-2))

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Honours), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 4th year

? Delivery Period : Semester 1 (Blocks 1-2)

? Contact Teaching Time : 2 hour(s) per week for 11 weeks

All of the following classes

Type	Day	Start	End	Area
Lecture	Tuesday	12:10	13:00	KB
Lecture	Friday	12:10	13:00	KB

Summary of Intended Learning Outcomes

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.