Here I am referring to http://demonstrations.wolfram.com/TheBelousovZhabotinskyReaction/, but not only this. If you press "Download demonstration as CDF" (implying you have the necessary tools to open it) and then look inside at the equations for that reaction. I have those myself.
A+Y -> X+P with rate constant k1 X+Y -> 2P with rate constant k2 A+X -> 2X+2Z with rate constant k3 2X -> A+P with rate constant k4 B+Z -> (1/2)fZ with rate constant k5
I have formulated these into differential equations, which is based on autocatalysis, for each of the intermediates
Z... Under here it is
z. I use * as multiplication, because I think it simplifies it a bit. This is done by treating the
B concentrations as constants.
dx/dt = k1*A*y-k2*x*y+k3*A*x-2*k4*x^2 dy/dt = -k1*A*y-k2*x*y+(1/2)*f*k5*B*z dz/dt = 2*k3*A*x-k5*B*z
Now, my question is: how are the above 3 differential equations converted to the dimensionless "3x3 system" following the Law of Mass Action (as what I referred to in the start of this post says)... What is done... what are the steps... how do you do this..!!?!?
I have researched the Law of Mass Action and all myself but I can't seem to find out what is done to reach the following from the above 3 differential equations:
ε* dx/dτ = q*y-x*y+x(1-x) δ* dy/dτ = -q*y-x*y+f*z dz/dτ = x-z
t is replaced by
τ, but what about the rest? Can anyone give me steps of what is happening?! I will appreciate it a lot! I included a picture to this post. The picture shows what I'm referring :)!