# DDE23 - specifying which variables are delayed

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Emse_ on 27 May 2024 at 6:33
Edited: Sanju on 27 May 2024 at 7:31
I am using dde23 and am unclear on how you specify which variables are lagged. Is this something you can specify? Does it go y1, y2, y3, y4? Can you set the order you want the des to appear in (I'm updating an existing set of code and am trying to avoid re-writing where unnecessary).
ETA: I found another example that gives me a hint - but I'm not sure I am right. Z is a n x m matrix, n = number of parameters, m = number of lag times specified.
So Z(2,1) is y2 lagged by 0.3 (the first lag option). Updating the code ...
% ExampleDDE - Matlab time dependent delay de
lags = [0.3 3]; % [y2 delay y4 delay]
tspan = [0 10];
param = [1 5 2 0.1 0.5 0.7]; % example parameters for DE
sol = dde23(@(t,y,z) ddefun(t,y,z,param), lags, @history, tspan);
plot(sol.x,sol.y,'-o')
xlabel('Time t');
ylabel('Solution y');
legend('y_1','y_2','y_3', 'y_4','Location','NorthWest');
function dydt = ddefun(t,y, Z, p)
y1 = y(1);
y2 = y(2);
y3 = y(3);
y4 = y(4);
ylag2 = Z(2,1); % this should be a delay on y2, first time lag
ylag4 = Z(4,2); % this should be a delay on y4, second time lag
lagged = ylag2/ylag4;
A = p(1);
B = p(2);
C = p(3);
a = p(4);
b = p(5);
d = p(6);
d1 = A* y1 + b * y3 - C * y4;
d2 = C * y4 + lagged * y3 - a * B * y4 - A * y1;
d3 = a * y4 - b * y3;
d4 = d * y4;
dydt = [d1;d2;d3;d4];
end
function s = history(t) % history function for t<= 0
s = [1 5 10 7];
end

Sanju on 27 May 2024 at 6:43
Hi Emse_,
In the dde23 function, you can specify which variables are lagged by providing the appropriate indices in the lags parameter. The indices correspond to the positions of the lagged variables in the state vector y.
For example, in your code snippet, lags = [0.3 3] indicates that y2 and y4 are lagged variables. The value 0.3 represents the delay for y2, and 3 represents the delay for y4.
The order of the lagged variables in the lags parameter should match the order of the corresponding variables in the state vector y. In your case, the state vector y is [y1; y2; y3; y4], so the lagged variables should be specified as [y2 delay; y4 delay].
You can set the order of the variables in the state vector y as per your requirement. However, make sure to update the ddefun function accordingly to access the variables correctly.
Emse_ on 27 May 2024 at 6:48
Thanks Sanju - do I have it correct with the edit I just made (my apologies for updating as you posted, you always find one more example after you give up and post)
Sanju on 27 May 2024 at 7:30
Edited: Sanju on 27 May 2024 at 7:31
The code you provided is correct and should work as intended.

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