How can I define and pass a history prior to t0 to dde23 ?
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In the documentation on dde23, it mentions that you can pass a history defined at t ≤ t0 to the solver, but in the examples it seems t ≤ 0 is the default for history. How can I change it from zero to t0?
Here's the example from the documentation:
function ddex1
%DDEX1 Example 1 for DDE23.
% This is a simple example of Wille' and Baker that illustrates the
% straightforward formulation, computation, and plotting of the solution
% of a system of delay differential equations (DDEs).
%
% The differential equations
%
% y'_1(t) = y_1(t-1)
% y'_2(t) = y_1(t-1)+y_2(t-0.2)
% y'_3(t) = y_2(t)
%
% are solved on [0, 5] with history y_1(t) = 1, y_2(t) = 1, y_3(t) = 1 for
% t <= 0.
%
% The lags are specified as a vector [1, 0.2], the delay differential
% equations are coded in the subfunction DDEX1DE, and the history is
% evaluated by the function DDEX1HIST. Because the history is constant it
% could be supplied as a vector:
% sol = dde23(@ddex1de,[1, 0.2],ones(3,1),[0, 5]);
%
% See also DDE23, FUNCTION_HANDLE.
% Jacek Kierzenka, Lawrence F. Shampine and Skip Thompson
% Copyright 1984-2004 The MathWorks, Inc.
sol = dde23(@ddex1de,[1, 0.2],@ddex1hist,[0, 5]);
figure;
plot(sol.x,sol.y)
title('An example of Wille'' and Baker.');
xlabel('time t');
ylabel('solution y');
% --------------------------------------------------------------------------
function s = ddex1hist(t)
% Constant history function for DDEX1.
s = ones(3,1);
% --------------------------------------------------------------------------
function dydt = ddex1de(t,y,Z)
% Differential equations function for DDEX1.
ylag1 = Z(:,1);
ylag2 = Z(:,2);
dydt = [ ylag1(1)
ylag1(1) + ylag2(2)
y(2) ];
Here's my own code:
t = [0:3000];
lags = 0.1;
hist = @(t) 0.000000001;
r = 0.1;
rm = 0.015;
Ka = 0.5;
Kb = 7;
K0 = 0.501;
sol = dde23(@(t,N,Nlag)Bilogistic(t,N,Nlag,Ka,Kb,r,rm,K0),lags,hist,[0,3000]);
tint = linspace(0,3000);
yint = deval(sol,tint);
plot(tint,yint,'r');
I would like to change the history so it reflects the range (-inf,t0).
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