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MA40045: Dynamical systems

Follow this link for further information on academic years Academic Year: 2017/8
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6      [equivalent to 12 CATS credits]
Further information on notional study hours Notional Study Hours: 120
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:
Like-for-like reassessment (where allowed by programme regulations)
Further information on requisites Requisites: Before taking this module you must take MA20221 AND ( take MA30041 OR take MA30062 )
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
(Poincaré 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 Mathematical Sciences