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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2011/2012
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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Dynamical Systems (MATH11027)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Course typeStandard AvailabilityAvailable to all students
Credit level (Normal year taken)SCQF Level 11 (Year 4 Undergraduate) Credits10
Home subject areaMathematics Other subject areaSpecialist Mathematics & Statistics (Honours)
Course website https://info.maths.ed.ac.uk/teaching.html Taught in Gaelic?No
Course descriptionCourse for final year students in Honours programmes in Mathematics.

Concepts of continuous and discrete dynamical systems. Orbits, fixed points and periodic orbits. Poincare maps. Classification of fixed points for linear discrete systems. Fixed points in nonlinear systems: stable and unstable manifolds. Bifurcation theory for one and two dimensional systems: saddle-node, flip and Hopf bifurcations. Logistic map: period-doubling cascade and chaos. Chaotic attractors and fractals.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Complex Variable & Differential Equations (MATH10033)
Co-requisites
Prohibited Combinations Other requirements None
Additional Costs None
Information for Visiting Students
Pre-requisitesNone
Displayed in Visiting Students Prospectus?Yes
Course Delivery Information
Delivery period: 2011/12 Semester 2, Available to all students (SV1) WebCT enabled:  Yes Quota:  None
Location Activity Description Weeks Monday Tuesday Wednesday Thursday Friday
King's BuildingsLectureJCMB, room 53261-11 11:10 - 12:00
King's BuildingsLectureJCMB, room 53261-11 11:10 - 12:00
First Class Week 18, Tuesday, 11:10 - 12:00, Zone: King's Buildings. JCMB, room 5326
Exam Information
Exam Diet Paper Name Hours:Minutes
Main Exam Diet S2 (April/May)Dynamical Systems2:00
Summary of Intended Learning Outcomes
1. Ability to identify and classify of fixed points of discrete systems.
2. Ability to construct of stable and unstable manifolds for nonlinear systems.
3. Ability to calculate an appropriate normal form for nonlinear systems and thereby deduce the stability of fixed points.
4. Ability to characterise saddle-node, flip and Hopf bifurcations.
5. Appreciation of the period-doubling cascade and the notion of chaotic systems.
6. Ability to calculate Liapunov exponents.
7. Familiarity with attractors and basins of attraction.
Assessment Information
Coursework: 15%; Degree Examination: 85%.
Visiting Student Variant Assessment
Coursework (15%); Examination (85%)
Special Arrangements
None
Additional Information
Academic description Not entered
Syllabus Not entered
Transferable skills Not entered
Reading list Not entered
Study Abroad Not entered
Study Pattern Not entered
KeywordsDSy
Contacts
Course organiserProf Jim Wright
Tel: (0131 6)50 8570
Email: J.R.Wright@ed.ac.uk
Course secretaryMrs Alison Fairgrieve
Tel: (0131 6)50 6427
Email: Alison.Fairgrieve@ed.ac.uk
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© Copyright 2011 The University of Edinburgh - 16 January 2012 6:25 am