Title

Semi-analytical solutions for reaction diffusion equations

Year

2015

Degree Name

Doctor of Philosophy

Department

School of Mathematics and Applied Statistics

Abstract

Semi-analytical solutions for three reaction-diffusion equation models are investigating in this thesis. The three models are the reversible Selkov, or glycolytic oscillations model, an extended Selkov model which incorporates the effects of a precursor chemical and final product and a Lotka-Volterra prey-predator system with two days.

The Galerkin method is applied, which approximates the spatial structure of the concentration or population densities. This approach is used to obtain a lower-order, ordinary differential equation model, for the system of governing equations. The semi-analytical model is analysed to obtain steady-state solutions, bifurcation diagrams and parameter maps in which the different types of birurcation patterns and Hopf bifurcations occur.

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