oregonator
Paul Cochrane
Example simulation of the Oregonator model of oscillating chemical
kinetics equations.
Calculates concentrations of components participating
in the Oregonator model. The reaction scheme is
A + Y ----> X + R (1)
X + Y ----> 2 R (2)
A + X ----> 2 X + 2 Z (3)
2 X ----> A + R (4)
B + Z ----> 1/2 Y (5)
Rate laws are
d[X]/dt = k1 [A] [Y] - k2 [X] [Y] + k3 [A] [X] - 2 k4 [X]^2
d[Y]/dt = -k1 [A] [Y] - k2 [X] [Y] + (1/2) k5 [B] [Z]
d[Z]/dt = 2 k3 [A] [X] - k5 [B] [Z]
which are transformed to
d[X]_d(tau) = (k1 [A] [Y] - k2 [X] [Y] + k3 [A] [X] - 2 k4 [X]^2)/(k5 [B])
d[Y]_d(tau) = (-k1 [A] [Y] - k2 [X] [Y] + (1/2) k5 [B] [Z])/(k5 [B])
d[Z]_d(tau) = (2 k3 [A] [X] - k5 [B] [Z])/(k5 [B])
where tau = k5*[B]*t is a unitless time variable. The
program integrates these equations, assuming that concentrations
of A and B are constant.
Adapted for xmds from "Mathematica computer programs for physical
chemistry", William H. Cropper, Springer Verlag (1998)
tau
yes
yes
yes
yes
main
1
main
double
CX CY CZ
RK4IP
50
5000
500
main