function sol = exam6
% exam6, exam6f of tutorial.

% This is a demonstration problem for CTMS/BD in 
% L. Tavernini, Continuous--Time Modeling and 
% Simulation, Gordon and Breach, Amsterdam, 1996.  
% It illustrates how to deal with the unusual
% situation of a solution discontinuous at the 
% initial point. Tavernini uses an initial y of 
% 19.00001, but we use 19.001 so as to see the 
% cyclic behavior sooner.

r = 3.5;
m = 19;
options = ddeset('RelTol',1e-4,'AbsTol',1e-7,...
                 'InitialY',19.001);
sol = dde23(@exam6f,0.74,19,[0, 40],options,r,m);
plot(sol.x,sol.y);
title('Population of Lemmings--Time Series')
xlabel('time t');
ylabel('y(t)');
figure
plot(sol.y,sol.yp)
title('Population of Lemmings--Phase Plane')
xlabel('y(t)');
ylabel('y''(t)');

%=================================================
function yp = exam6f(t,y,Z,r,m)
yp = r*y*(1 - Z/m);