Tue Feb 10 12:28:03 2004 run on Linux
% Examples for the conversion of reaction equations to ordinary
% differential equations.
% Example taken from Feinberg (Chemical Engineering):
species := {A1,A2,A3,A4,A5};
species := {a1,
a2,
a3,
a4,
a5}
reac2ode { A1 + A4 <> 2A1, rho, beta,
A1 + A2 <> A3, gamma, epsilon,
A3 <> A2 + A5, theta, mue};
2
{df(a1,t)=rho*a1*a4 - beta*a1 - gamma*a1*a2 + epsilon*a3,
df(a2,t)= - gamma*a1*a2 + epsilon*a3 + theta*a3 - mue*a2*a5,
df(a3,t)=gamma*a1*a2 - epsilon*a3 - theta*a3 + mue*a2*a5,
2
df(a4,t)= - rho*a1*a4 + beta*a1 ,
df(a5,t)=theta*a3 - mue*a2*a5}
inputmat;
[1 0 0 1 0]
[ ]
[1 1 0 0 0]
[ ]
[0 0 1 0 0]
outputmat;
[2 0 0 0 0]
[ ]
[0 0 1 0 0]
[ ]
[0 1 0 0 1]
% Computation of the classical reaction matrix as difference
% of output and input matrix:
reactmat := outputmat-inputmat;
[1 0 0 -1 0]
[ ]
reactmat := [-1 -1 1 0 0]
[ ]
[0 1 -1 0 1]
% Example with automatic generation of rate constants and automatic
% extraction of species.
species := {};
species := {}
reac2ode { A1 + A4 <> 2A1,
A1 + A2 <> A3,
A3 <> A2 + A5};
new species: a1
new species: a4
new species: a2
new species: a3
new species: a5
2
{df(a1,t)= - a1 *rate(2) + a1*a4*rate(1) - a1*a2*rate(3) + a3*rate(4),
2
df(a4,t)=a1 *rate(2) - a1*a4*rate(1),
df(a2,t)= - a1*a2*rate(3) - a2*a5*rate(6) + a3*rate(5) + a3*rate(4),
df(a3,t)=a1*a2*rate(3) + a2*a5*rate(6) - a3*rate(5) - a3*rate(4),
df(a5,t)= - a2*a5*rate(6) + a3*rate(5)}
on rounded;
species := {};
species := {}
reac2ode { A1 + A4 <> 2A1, 17.3* 22.4**1.5,
0.04* 22.4**1.5 };
new species: a1
new species: a4
2
{df(a1,t)= - 4.24064598853*a1 + 1834.07939004*a1*a4,
2
df(a4,t)=4.24064598853*a1 - 1834.07939004*a1*a4}
end;
Time for test: 1 ms