Chapter 10
The Brusselator
In the Beginning the Heav’ns and Earth Rose out of Chaos.
(P.L. Milton, 1667)
10.1 Brusselator Model Equations
One important characteristic of real-world processes is that interactions among
system components are nonlinear. As we have seen in the previous chapters, nonlinearities can give rise to rich temporal patterns. An example of nonlinearities in
chemical reactions is the autocatalytic process
A þ X ! 2X
ð10:1Þ
whereby X stimulates its own production from A. Such autocatalytic reactions may
involve a series of intermediate sates, for example if X produces a substance Y,
which in turn accelerates the production of X. One such cross-catalytic reaction has
been studied extensively by a group of scientists around the Nobel Laureate Ilya
Prigogine in Brussels, and is known as the Brusselator [1]. It involves the following
series of reaction steps:
A ! X
ð10:2Þ
2X þ Y ! 3X
ð10:3Þ
A save-disabled version of STELLA and the computer models of this book are available at
www.iseesystems.com/modelingdynamicbiologicalsystems.
B. Hannon and M. Ruth, Modeling Dynamic Biological Systems,
Modeling Dynamic Systems, DOI 10.1007/978-3-319-05615-9_10,
© Springer International Publishing Switzerland 2014
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