Code covered by the BSD License
 exam1
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 exam3
 exam4
 exam4
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This is a demonstration problem for CTMS/BD in
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This is a demonstration problem for CTMS/BD in
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An example from C. Marriott and C. DeLisle, Effects
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An example from C. Marriott and C. DeLisle, Effects
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This is the suitcase problem from Suherman, et al.,
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This is the suitcase problem from Suherman, et al.,
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Example 1 of K.W. Neves, Automatic integration
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Example 1 of K.W. Neves, Automatic integration
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Example of J.D. Farmer, Chaotic Attractors of an
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Example of J.D. Farmer, Chaotic Attractors of an
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Wheldon's model of chronic granuloctic leukemia
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Wheldon's model of chronic granuloctic leukemia
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Sample problem of ARCHI manual. The absolute error
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Sample problem of ARCHI manual. The absolute error
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Marchuk immunology model of E. Hairer, S.P. Norsett, and
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Marchuk immunology model of E. Hairer, S.P. Norsett, and
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This system of ODE's is taken from 'An Introduction to Nuermcial Methods
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This system of ODE's is taken from 'An Introduction to Nuermcial Methods
 prob2
This problem considers a cardiovascular model, which can be found in
 prob2
This problem considers a cardiovascular model, which can be found in
 prob2b
This problem considers a cardiovascular model, which can be found in
 prob2b
This problem considers a cardiovascular model, which can be found in
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This problem is epidemic model due to Cooke, more information can be
 prob3
This problem is epidemic model due to Cooke, more information can be
 prob4
This problem is an epidemic model due to Cooke et alia, more information
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This problem is an epidemic model due to Cooke et alia, more information
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This problem population growth model due to Cooke et alia, more information
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This problem population growth model due to Cooke et alia, more information

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Tutorial on solving DDEs with DDE23
by
Jacek Kierzenka
22 Aug 2003
(Updated
12 Oct 2010)
Solving delay differential equations with DDE23. Tutorial + Examples.

prob2

function sol = prob2
% This problem considers a cardiovascular model, which can be found in
% 'Modelling of the BaroflexFeedback Mechanism With TimeDelay' by J.T.
% Ottesen in J. Math. Biol., 36 (1997), 4163. (This is reference
% 14 of the tutorial).
% Copyright 2004, The MathWorks, Inc.
% Problem parameters, visible in nested functions.
p.ca = 1.55;
p.cv = 519;
p.R = 1.05;
p.r = 0.068;
p.Vstr = 67.9;
p.alpha0 = 93;
p.alphas = 93;
p.alphap = 93;
p.alphaH = 0.84;
p.beta0 = 7;
p.betas = 7;
p.betap = 7;
p.betaH = 1.17;
p.gammaH = 0;
P0 = 93;
Paval = P0;
Pvval = (1 / (1 + p.R/p.r)) * P0;
Hval = (1 / (p.R * p.Vstr)) * (1 / (1 + p.r/p.R)) * P0;
history = [Paval; Pvval; Hval];
for tau = [1 7.5]
sol = dde23(@prob2f,tau,history,[0, 350]);
figure
plot(sol.x,sol.y(1,:))
title(['Problem 2. Baroflex Feedback Mechanism with' ...
' \tau = ',num2str(tau),'.'])
xlabel('time t')
ylabel('P_a(t)')
axis([0 350 82 96])
end
%
% Nested function
%
function yp = prob2f(t,y,Z)
%PROB2F The derivative function for Problem 2 of the DDE Tutorial.
% Local variables are used to express the equations in terms
% of the physical quantities of the model.
ylag = Z(:,1);
Patau = ylag(1);
Paoft = y(1);
Pvoft = y(2);
Hoft = y(3);
dPadt =  (1 / (p.ca * p.R)) * Paoft + (1/(p.ca * p.R)) * Pvoft ...
+ (1/p.ca) * p.Vstr * Hoft;
dPvdt = (1 / (p.cv * p.R)) * Paoft ...
 ( 1 / (p.cv * p.R) + 1 / (p.cv * p.r) ) * Pvoft;
Ts = 1 / ( 1 + (Patau / p.alphas)^p.betas );
Tp = 1 / ( 1 + (p.alphap / Paoft)^p.betap );
dHdt = (p.alphaH * Ts) / (1 + p.gammaH * Tp)  p.betaH * Tp;
yp = [ dPadt;
dPvdt;
dHdt ];
end % prob2f
%
end % prob2


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