The Brusselator

Abstract

One important charactersitic 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,

$$ {\text{A + X}} \to {\text{2X,}} $$

(1)

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 Brusselator¹. It involves the following series of reaction steps:

$$ {\text{A}} \to {\text{X}} $$

(2)

$$ {\text{2X + Y}} \to 3{\text{X}} $$

(3)

$$ {\text{B + X}} \to {\text{Y + D}} $$

(4)

$$ {\text{X}} \to {\text{E}} $$

(5)

In the Beginning the Heav’ns and Earth Rose out of Chaos. P.L.Milton, 1667