function [ sol1 sol2 ] = prob_4_9(tau)
% PROB_4_9 - 
% 
% Written by:
% -- 
% John L. Weatherwax                2005-04-27
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

a=0.25; b=-0.01; c=-1.0; d=0.01; m=200; 

y0 = [ 80 30 ];

options = ddeset( 'RelTol', 1e-5, 'AbsTol', 1e-8 );

sol1 = dde23(@odes,[],y0,[0 100],options,a,b,c,d,m);
sol2 = dde23(@ddes,[tau],y0,[0 100],options,a,b,c,d,m);

figure; 
h1=plot( sol1.y(1,:), sol1.y(2,:), '-go' ); hold on; 
h2=plot( sol2.y(1,:), sol2.y(2,:), '-ro' ); grid on; 
xlabel( 'y_1(t)' ); ylabel( 'y_2(t)' ); 
title( [ 'Tau = ', num2str(tau) ] );
legend( [h1,h2], 'No Delay', 'Delay' ); 

function v = odes(t,y,z,a,b,c,d,m)
% ODES - 
% 

v = [ a*y(1) + b*y(1)*y(2);
      c*y(2) + d*y(1)*y(2); ];

function v = ddes(t,y,z,a,b,c,d,m)
% DDES - 
% 

% With resource term:
% $$$ v = [ a*y(1)*(1-y(1)/m) + b*y(1)*y(2);
% $$$       c*y(2) + d*z(1,1)*z(2,1); ];

% Without resource term:
v = [ a*y(1) + b*y(1)*y(2);
      c*y(2) + d*z(1,1)*z(2,1); ];