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2010/1 Module Catalogue
 Module Code: MAT3007 Module Title: NONLINEAR DYNAMICS AND CHAOS
Module Provider: Mathematics Short Name: MS304
Level: HE3 Module Co-ordinator: LLOYD D Dr (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 a test and an assignment which will involve the use of Maple.
Exam: Written examination (2 hours, unseen).
Qualifying Condition(s) 
            A weighted aggregate mark of 40% is required to pass the module.

Module Overview


Module Aims

Introduce the main features of nonlinear dynamical systems (with applications) and techniques for analysing such systems.

Learning Outcomes

At the end of the course, students should be able to
• Analyse simple bifurcations in nonlinear dynamical systems
• Analyse the common routes to chaos in dynamical systems, and
• Analyse simple chaotic iterated maps.

Module Content

The course covers the following topics:
• Topological dynamics of ordinary differential equations
• Saddle-node, transcritical, pitchfork, Hopf, period-doubling and homoclinic bifurcations of ordinary differential equations
• One-dimensional iterated maps, bifurcations and topological conjugacy
• Period-doubling route to chaos, universality and renormalisation in 1D iterated maps
• Lyapunov exponents and sensitive dependence on initial conditions of 1D iterated maps
• Chaotic 1D maps (Doubling and tent maps) and symbolic dynamics
• Fractal geometry and non-integer dimension
• Strange attractors and repellers
• Applications: population dynamics, classical mechanics, chemical oscillations etc.

Methods of Teaching/Learning

Teaching is by lectures and tutorials. Learning takes place through lectures, tutorials, exercises, coursework and background reading. 3 lecture/tutorial hours per week for 10 weeks.

Selected Texts/Journals

Further Reading
Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Steven H. Strogatz, Westview, 2000.
Does God play Dice?, Ian Stewart, Oxford Press, 1989.
Mathematical Biology: Part I, J. D. Murray, Springer-Verlag, 2002.

Last Updated

14 September 2009