Control of Spiral Waves in Reaction-Diffusion Systems Using Response Function
Almuaddi, S
Date: 16 December 2019
Publisher
University of Exeter
Degree Title
the degree of Doctor of Philosophy in Mathematics
Abstract
This thesis is motivated by the desire to understand spiral wave dynamics in reactiondiffusion systems with particular focus on the FitzHugh-Nagumo model. We attempt to control the behaviour of spiral waves using controller dynamics. Response functions characterise the behaviour of spiral waves under perturbations, and so it is natural ...
This thesis is motivated by the desire to understand spiral wave dynamics in reactiondiffusion systems with particular focus on the FitzHugh-Nagumo model. We attempt to control the behaviour of spiral waves using controller dynamics. Response functions characterise the behaviour of spiral waves under perturbations, and so it is natural to use these for control purposes. In this project, we consider perturbations of the FitzHugh-Nagumo equation using control functions with different support. We calculate the response functions using the adjoint linear system of the FitzHugh-Nagumo equation with 1D controller dynamics and also characterise the control functions with the smallest support function which can be used to control the system in periodic and meander regimes. We find the minimum size of the support function that the radius is comparable to the region of the non zero response function.
Doctoral Theses
Doctoral College
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