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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
Credit level (Normal year taken)SCQF Level 11 (Year 4 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryCourse 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.
Course description Not entered
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
Information for Visiting Students
Pre-requisitesNone
High Demand Course? Yes
Course Delivery Information
Not being delivered
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.
Reading List
None
Additional Information
Course URL https://info.maths.ed.ac.uk/teaching.html
Graduate Attributes and Skills Not entered
KeywordsDSy
Contacts
Course organiserDr Jacques Vanneste
Tel: (0131 6)50 6483
Email:
Course secretaryMrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email:
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