% 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('Figure 6a. Population of Lemmings--Time Series')
xlabel('time t');
ylabel('y(t)');
figure
plot(sol.y,sol.yp)
title('Figure 6b. Population of Lemmings--Phase Plane')
xlabel('y(t)');
ylabel('y''(t)');