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2010/1 Module Catalogue
 Module Code: MAT3030 Module Title: CHAOTIC DYNAMICS
Module Provider: Mathematics Short Name: MAT3030
Level: HE3 Module Co-ordinator: MELBOURNE I Prof (Maths)
Number of credits: 15 Number of ECTS credits: 7.5
Module Availability
Assessment Pattern
Unit(s) of Assessment
Weighting Towards Module Mark( %)
Coursework: in the form of exercises and class sheets
Exam: Written examination (2 hours, unseen)
Qualifying Condition(s) 
An overall aggregate mark of 40% for the module is required to pass the module.
Module Overview
The module introduces nonlinear dynamics and chaos for discrete dynamical systems focusing on maps of the interval and circle.
Desirable: Ordinary Differential Equations.
Module Aims
Learning Outcomes

At the end of the module, a student should be able to: 

(1) Analyse simple dynamics (fixed points, periodic points, and their stability) and associated bifurcations
(2) Analyse simple chaotic maps 
(3) Recognise the common routes to chaos.

Module Content

Fixed points and periodic orbits.  Stability.   Saddle-node and period-doubling bifurcations. Topological transitivity, sensitive dependence on initial conditions.    Topological conjugacy and symbolic dynamics.   Lyapunov exponents.   Period-doubling route to chaos, universality and renormalisation.

Methods of Teaching/Learning
3 contact hours per week for 10 weeks.  Teaching is by lectures and tutorials.  Learning takes place through lectures, tutorials, exercises and background reading.
Selected Texts/Journals

R.L.Devaney.   An Introduction to Chaotic Dynamical Systems, Addison-Wesley, 1989 
S.H. Strogatz.  Nonlinear Dynamics and Chaos.   Westview 2000
Popular reading 
I.N. Stewart.  Does God Play Dice?  Oxford Press, 1989.

Last Updated

21 March 2011