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Title: Orbit space reduction for symmetric dynamical systems with an application to laser dynamics
Author: Crockett, Victoria Jane
ISNI:       0000 0004 2713 2644
Awarding Body: University of Exeter
Current Institution: University of Exeter
Date of Award: 2010
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This work considers the effect of symmetries on analysing bifurcations in dynamical systems. We consider an example of a laser with strong optical feedback which is modelled using coupled non-linear differential equations. A stationary point can be found in space, which can then be continued in parameter space using software such as AUTO. This software will then detect and continue bifurcations which indicate change in dynamics as parameters are varied. Due to symmetries in the equations, using AUTO may require the system of equations to be reduced in order to study periodic orbits of the original system as (relative) equilibria of the reduced system. Reasons for this are explored as well as considering how the equations can be changed or reduced to remove the symmetry. Invariant and Equivariant theory provide the tools for reducing the system of equations to the orbit space, allowing further analysis of the lasers dynamics.
Supervisor: Wieczorek, Sebastian Sponsor: Great Western Research ; Bookham Technology
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Laser Dynamics ; Dynamical Systems ; Orbit Space Reduction ; Symmetric Dynamical Systems