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| Module Availability |
| Spring |
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| Assessment Pattern |
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Unit(s) of Assessment
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Weighting Towards Module Mark( %)
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Coursework: in the form of exercises and class sheets
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25
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Exam: Written examination (2 hours, unseen)
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75
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Qualifying Condition(s)
An overall aggregate mark of 40% for the module is required to pass the module.
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| Module Overview |
| The module introduces nonlinear dynamics and chaos for discrete dynamical systems focusing on maps of the interval and circle. |
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| Prerequisites/Co-requisites |
| Desirable: Ordinary Differential Equations. |
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| Module Aims |
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| 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. |
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| 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. |
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| 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. |
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| 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. |
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| Last Updated |
| 18th October 2010 |
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