Mathematical models of chemical reactions illustrating Hopf bifurcations and oscillatory behaviour: A. The Belousov-Zhabotinski reaction. B. An enzyme-catalysed reaction known as the S-A system

Abstract

This thesis gives a detailed and much expanded account of the following two papers, filling in details of the proofs, and using Maple for numerical work: Hastings, S.P. and Murray, J.D. 1975. 'The Existence of Oscillatory Solutions in the Field-Noyes Model for the Belousov-Zhabotinski Reactions', SIAM Journal of Applied Mathematics, 28(3), pp. 678-688. Hassard, B. and Jiang, K. 1992. 'Unfolding a Point of Degenerate Hopf Bifurcation in an Enzyme-catalyzed Reaction Model', SIAM Journal of Mathematical Analysis, 23(5), pp. 1291-1304. Two different chemical reactions, each of which are modelled by systems of ordinary differential equations, are examined to show that Hopf bifurcations occur at certain parameter values, giving rise to periodic solutions.