Module manager: Dr T. Wagenknecht
Email: thomas@maths.leeds.ac.uk
Taught: Semester 2 (Jan to Jun) View Timetable
Year running 2008/09
MATH1035 and (MATH1015 or MATH1060 or MATH1331) and (MATH1915 or MATH1916 or MATH1917). MATH2391 is helpful but not essential.
| MATH5396M | Advanced Dynamical Systems |
This module is 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 |
|---|---|---|---|
| Example Class | Delivery type 6 | Number 1 | Length hours 6 |
| Lecture | Delivery type 27 | Number 1 | Length hours 27 |
| Private study hours | Delivery type 117 | ||
| Total Contact hours | Delivery type 33 | ||
| Total hours (100hr per 10 credits) | Delivery type 150 | ||
Five example sheets.
| Assessment type | Notes | % of formal assessment |
|---|---|---|
| Assessment type Computer Exercise | Notes . | % of formal assessment 15 |
| Total percentage (Assessment Coursework) | Assessment type 15 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
| Exam type | Exam duration | % of formal assessment |
|---|---|---|
| Exam type Standard exam (closed essays, MCQs etc) | Exam duration 3.0 Hrs Mins | % of formal assessment 85 |
| Total percentage (Assessment Exams) | Exam type 85 | |
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: 25/07/2008
Errors, omissions, failed links etc should be notified to the Catalogue Team