MAGIC059: Dynamical Systems I (Flows)

Course details

A core MAGIC course

Semester

Autumn 2013
Monday, October 7th to Saturday, December 14th

Hours

Live lecture hours
10
Recorded lecture hours
0
Total advised study hours
0

Timetable

Tuesdays
09:05 - 09:55

Description

Many problems in Applied Mathematics are nonlinear and described by nonlinear ordinary (or partial) differential equations. This course aims to introduce students to the tools and techniques needed to understand the dynamics that might arise in such systems. The emphasis will be on concepts and examples rather than theorems and proofs, and will include a brief survey of useful numerical methods and packages. Students will be invited to submit examples of their own for possible discussion.

Prerequisites

No explicit prerequisites beyond standard undergraduate mathematics.

Syllabus

Outline syllabus
* Definition of a flow (ordinary differential equation), invariant sets, limit sets
* The Poincaré Map
* Equilibria, linearisation, stability of equilibria, periodic orbits and other invariant sets
* Structural stability, Hartman-Grobman Theorem, stable and unstable manifolds
* Centre manifold theorem, local bifurcations of equilibria and periodic orbits,
* Birkhoff normal form transformations for equilibria
* Examples from chemistry, population dynamics, mechanics

Lecturer

  • Dr Jan Sieber

    Dr Jan Sieber

    University
    University of Exeter

Bibliography

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Assessment

Description

The assessment for this course will be a single take-home paper in January and with 2 weeks to complete and submit online. There will be 3 questions. All questions have to be attempted, and you will need overall 60

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Files

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Lectures

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