Module manager: Dr Jitse Niessen
Email: J.Niesen@leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2024/25
(MATH2016 or MATH2017) and (MATH1012 or MATH1060 or MATH1331). MATH2391 is helpful but not required.
| MATH5395M | Advanced Dynamical Systems |
| MATH5396M | Advanced Dynamical Systems |
This module is not approved as an Elective
This course continues the study of nonlinear dynamics begun in MATH 2391, but for maps rather than differential equations. Maps are the natural setting for understanding the nature of chaotic dynamics, which arise in a variety of contexts in biology, chemistry, physics, economics and engineering.
On completion of this module, students should be able to:
a) find fixed points, periodic orbits and other invariant sets in maps and compute their stability;
b) understand the structure of chaos in maps;
c) use a computer to investigate the behaviour of families of one-dimensional maps;
d) transform between the dynamics of a one-dimensional maps (the Lorenz map, the tent map and the logistic map) and symbolic dynamics;
e) identify codimension-one bifurcations in maps and sketch bifurcation diagrams;
f) use renormalisation techniques to understand the cascades of bifurcations involved in the transition to chaos.
- One-dimensional maps: fixed points, periodic points, asymptotic and Lyapunov stability, Lyapunov exponent, omega-limit sets, conjugate maps, topological entropy, topological chaos and horse-shoes, Period-three implies chaos, sensitive dependence on initial conditions, Schwartzian derivative, renormalisation, the period-doubling cascade and Feigenbaum's constant.
- Maple programs will be used throughout to demonstrate important principles.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lecture | 33 | 1 | 33 |
| Private study hours | 117 | ||
| Total Contact hours | 33 | ||
| Total hours (100hr per 10 credits) | 150 | ||
Studying and revising of course material.
Completing of assignments and assessments.
Five example sheets.
| Exam type | Exam duration | % of formal assessment |
|---|---|---|
| Open Book exam | 2.0 Hrs 30 Mins | 100 |
| Total percentage (Assessment Exams) | 100 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
The reading list is available from the Library website
Last updated: 4/29/2024
Errors, omissions, failed links etc should be notified to the Catalogue Team