- Student Records
Programme & Unit Catalogues

MA40045: Dynamical systems

Follow this link for further information on academic years Academic Year: 2015/6
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 module 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 2015/16 academic year only. Students continuing their studies into 2016/17 and beyond should not assume that this unit will be available in future years in the format displayed here for 2015/16.
* 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.