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:
 Write the system of 2 coupled differential equations for the intermediate concentrations [X] and [Y].
 (b) Let each of the rate constants k_{i} = 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).
 (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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