# Mackey Glass equation and ddesd

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Amir Mahmoudi on 19 Sep 2023
Commented: Amir Mahmoudi on 20 Sep 2023
I am trying to extract Mackey-Glass attrcator through ddesd package. Initially, I need the series, so here are my codes
sol = ddesd(@ddefun,@delay,@history,[0 30000]);
t = sol.x;
x = sol.y;
plot(t,x);
x0 = rand;
function dxdt = ddefun(t,x,Z)
dxdt = 2*Z/(1 + Z^(9.65)) - x;
end
function d = delay(t,x)
d = t - 2;
end
function v = history(t)
v = 0;
end
Sadly, I get no series. I do not know what I have missed out. I genuinely ask for your help.

Steven Lord on 19 Sep 2023
So in these equations you're using the Equation 2 form where is 2, θ is 1, n is 9.65, τ is 2, and γ is 1?
If the density of the cells starts off at P(t) = 0 (as is the case based on your history function) why do you expect any cells to spontaneously come into existence? If I changed your history and the time over which I solved the system (to fit in the time restrictions of MATLAB Answers) I got a non-constant answer. Whether or not this is correct is something for you to determine.
If you're going to generalize this I'd define the parameters as constant values in ddefun (or have ddefun accept them as additional parameters) to make it easier to modify the equations (simply by changing the parameter values, rather than changing the equations.) I did this for two of the parameters, n and tau.
sol = ddesd(@ddefun,@delay,@history,[0 30]); % Changed from 30000 to 30
t = sol.x;
x = sol.y;
plot(t,x);
function dxdt = ddefun(t,x,Z)
n = 9.65;
dxdt = 2*Z/(1 + Z^n) - x;
end
function d = delay(t,x)
tau = 2;
d = t - tau;
end
function v = history(t)
v = 0.5; % Changed from 0 to 0.5
end
Amir Mahmoudi on 20 Sep 2023
This is what i was looking for. Thanks a lot.

Torsten on 19 Sep 2023
Moved: Torsten on 19 Sep 2023
I'm not sure what you are exactly asking for, but for a history v = 0, the solution is v = 0 for all times t > 0.
So the plot you get is correct.