Chapter 10

The Belousov-Zhabotinskii reaction

The reaction mechanism is described, and the Field, Körös, Noyes model (the Oregonator) is given. It is then scaled and relaxation oscillations are analysed. The notes and references give a variety of recipes, of which I have used Lou Howard's, mainly for oscillations, and Winfree's for waves. I think I also used Tyson's recipe (I remember weighing out the ingredients!) for oscillations.

I tend to have trouble with ferroin, though in fact the clear to yellow transition of the cerium is quite visible on its own. Maybe this is because my chemicals are now rather aged!

It is worth remembering that the FKN model is an extreme condensation of their chemical mechanism. Question 5 of the exercises asks for an analysis of a seven variable model proposed by Argoul et al., which they used in a chemostat to explain chaotic oscillations. However, when I went through this question (just the once) in a class, it turned out that the model made no sense without the continuous flow assumption...or so it seemed.

John Tyson offered very useful comments on this chapter; one of these was to suggest that the scaling analysis, which follows Murray's 1977 book (not the 1989 one), was outmoded and it is better to follow his (Tyson's) 1985 scaling. Question 10 concerns this, though my feeling is that there is no significant difference to be obtained, and the matter is one of taste. However, the issue is also one which is central to the theme of this book.