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MA40045: Dynamical systems

[Page last updated: 23 October 2023]

Academic Year: 2023/24
Owning Department/School: Department of Mathematical Sciences
Credits: 6 [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Masters UG & PG (FHEQ level 7)
Period:
Semester 1
Assessment Summary: EX 100%
Assessment Detail:
  • Examination (EX 100%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must take MA20221
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.


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.

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

Content: 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).

Course availability:

MA40045 is Optional on the following courses:

Department of Mathematical Sciences

Notes:

  • This unit catalogue is applicable for the 2023/24 academic year only. Students continuing their studies into 2024/25 and beyond should not assume that this unit will be available in future years in the format displayed here for 2023/24.
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