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General


This course is part of the MAGIC core.

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.

Semester

Autumn 2016 (Monday, October 3 to Friday, December 9)

Timetable

  • Tue 09:05 - 09:55

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


Jan Sieber
Email J.Sieber@exeter.ac.uk
Phone 01392 723973
vcard
Photo of Jan Sieber
Profile: Interests : nonlinear dynamics, applications


Students


Photo of Jacob Brooks
Jacob Brooks
(Surrey)
Photo of Adam Crowder
Adam Crowder
(Manchester)
Photo of Lamees Felemban
Lamees Felemban
(Exeter)
Photo of Xiao Ma
Xiao Ma
(Loughborough)
Photo of Puneet Matharu
Puneet Matharu
(Manchester)
Photo of Joel Mitchell
Joel Mitchell
(Birmingham)
Photo of Hannah Pybus
Hannah Pybus
(Nottingham)
Photo of Marzia Romano
Marzia Romano
(Northumbria)
Photo of Fabio Strazzeri
Fabio Strazzeri
(Southampton)
Photo of Robert West
Robert West
(Leeds)
Photo of Patrick WRIGHT
Patrick WRIGHT
(Leeds)
Photo of Adam Yorkston
Adam Yorkston
(East Anglia)


Bibliography


Elements of applied bifurcation theoryKuznetsov


Note:

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Assessment



The assessment for this course will be via a single take-home paper in January with 2 weeks to complete and submit online. Satisfactory answers to all three questions will achieve a passing grade. You are welcome to use your notes, solutions to examples sheets, online resources, and symbolic algebra to complete the questions.

Take-home examination

Files:Exam paper
Released: Monday 9 January 2017 (44.6 days ago)
Deadline: Sunday 22 January 2017 (30.6 days ago)
Instructions:

The assessment for this course will be via a single take-home paper in January with 2 weeks to complete and submit online. Satisfactory attempts at all three questions will achieve a passing grade. You are welcome to use your notes, solutions to examples sheets, online resources, and symbolic algebra to complete the questions.



Files


Files marked L are intended to be displayed on the main screen during lectures.

Week(s)File
1-10beam.avi
1-10exercises_I.pdf
1-10exercises_II.pdf
1-10exercises_III.pdf
1-10exercises_IV.pdf
1-10General_Transformation+Hopf_example.pdf
1-10Hopf-normalform-calculations.pdf
1-10Hopf_example.pdf
1-10js_ds1.pdf
1-10non-generic-bifurcations.pdf
1-10StickSlipExperimentShort.avi


Recorded Lectures


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