# 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 .