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MA40045: Dynamical systems

Follow this link for further information on academic years Academic Year: 2014/5
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6
Further information on unit levels Level: Masters UG & PG (FHEQ level 7)
Further information on teaching periods Period: Semester 1
Further information on unit assessment Assessment Summary: EX 100%
Further information on unit assessment Assessment Detail:
  • Examination (EX 100%)
Further information on supplementary assessment Supplementary Assessment: MA40045 Mandatory extra work (where allowed by programme regulations)
Further information on requisites Requisites: Before taking this unit you must take MA20216 and take MA20218 and take MA20219 and take MA20220 and take MA20221 and take MA30041. Students may also find it useful to take MA40062 before taking this unit.
Further information on descriptions Description: Aims:
To provide an accessible introduction to the qualitative and geometric theory of dynamical systems to a level that will make accessible an area of mathematics that is highly active and reaches into many areas of applied mathematics.

Learning Outcomes:
Students should be conversant with concepts, results and techniques fundamental to the study of the qualitative behaviour of continuous-time dynamical systems. Students should be able to investigate stability of equilibria and periodic orbits and should have a basic understanding and appreciation of invariant manifolds and bifurcations.

Numeracy T/F A
Problem Solving T/F A
Written and Spoken Communication F (in tutorials)

Linearisation and Hyperbolicity
(stability, conjugacies, and the stable manifold theorem),
Periodic solutions and the dynamics in the plane
(PoincarĂ© index and the Poincaré Bendixon Theorem),
Bifurcations from equilibria
(Centre manifold theorem, the saddle-node, transcritical and Hopf bifurcation),
Global bifurcations
(homoclinic orbits, homoclinic bifurcations).
Further information on programme availabilityProgramme availability:

MA40045 is Optional on the following programmes:

Department of Computer Science
  • USCM-AFM14 : MComp(Hons) Computer Science and Mathematics (Year 4)
  • USCM-AAM14 : MComp(Hons) Computer Science and Mathematics with Study year abroad (Year 5)
  • USCM-AKM14 : MComp(Hons) Computer Science and Mathematics with Year long work placement (Year 5)
Department of Mathematical Sciences
* This unit catalogue is applicable for the 2014/15 academic year only. Students continuing their studies into 2015/16 and beyond should not assume that this unit will be available in future years in the format displayed here for 2014/15.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.