Department of Mathematics

IDEA: Internet Differential Equations Activities

Brusselator model of Oscillating Chemical Reactions

Brusselator model of Oscillating Chemical Reactions

The Brusselator model was proposed by I. Pregogine and his collaborators at the Free University of Brussels. The reaction mechanism and corresponding rates are:

step

molecular reaction

step contribution to rate laws

1

A X

2

2X+Y 3X

3

B + X Y + D

4

X E

The net reaction is A+BC+D with transient appearance of intermediates X and Y.

Problem:

  1. Write the system of 2 coupled differential equations for the intermediate concentrations [X] and [Y].
  2. (b) Let each of the rate constants ki = 1 and assume the two reactants A and B have constant concentrations, [A]=1 and [B]=3 (they are added to the system at the same rate as they are consumed in the reactions). Choose initial concentrations for intermediates ([X]0 = 1, [Y]0=1), and perform a numerical integration from time 0 to 50 (arbitrary units).
  3. (c) Make two plots of the results: -log([X]) and -log([Y]) versus time, and -log([Y]) versus -log([X]).

For a solution of this problem, see the interactive mathcad file brussels.mcd .

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