brusselator
Paul Cochrane
Example simulation of the Brusslator model oscillating chemical
kinetics equations.
Calculates concentrations of components participating
in the autocatalytic Brusselator model. The reaction scheme is
A ----> X (1)
B + X ----> R + Y (2)
Y + 2 X ----> 3 X (3)
X ----> S. (4)
Rate equations for the intermediates X and Y are
d[X]/dt = k1[A] - k2 [B] [X] + k3 [X]^2 [Y] - k4 [X]
d[Y]/dt = k2 [B] [X] - k3 [X]^2 [Y],
which are transformed in the program to
d[X]/d(tau) = (k1[A] - k2 [B] [X] + k3 [X]^2 [Y] - k4 [X])/k4
d[Y]/d(tau) = (k2 [B] [X] - k3[X]^2 [Y])/k4,
with tau = k4 t a unitless time-related variable.
Adapted for xmds from "Mathematica computer programs for physical
chemistry", William H. Cropper, Springer Verlag (1998)
Equations are:
d[X]_d(tau) = (k1[A] - k2[B][X] + k3[X]^2 [Y] - k4[X])/k4
d[Y]_d(tau) = (k2[B][X] - k3[X]^2 [Y])/k4
tau
yes
yes
yes
yes
main
1
main
double
CX CY
RK4IP
250
5000
500
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