echo on
clc
%	ODE23 and ODE45 are functions for the numerical solution of
%	ordinary differential equations.  They employ automatic step
%	size Runge-Kutta-Fehlberg integration methods.  ODE23 uses a
%	simple 2nd and 3rd order pair of formulas for medium accuracy
%	and ODE45 uses a 4th and 5th order pair for higher accuracy.

pause	% Strike any key to continue.
clc
%	Consider rabbits and foxes
%          r'(t) = 2*r - alfa * r * f
%          f'(t) = -f + alfa * r * f
%	   r(0) = r0;	f(0) = r0
alfa=input('enter alfa for rabbits and foxes (e.g. .01) ' );
r0=input('enter initial rabbit population (e.g. 300) ');
f0=input('enter initial fox population (e.g. 150) ' );

% share the variable alfa between 'driver' and derivative routine 'rabfox'
global alfa
%
%
disp('the m file with derivatives ');
type rabfox

clc
%	To simulate the differential equation defined in RABFOX over the
%	interval	0 < t < 10, we invoke ODE23:

t0 = 0;
tfinal=input('enter final value of time (e.g. 12)');
y0 = [r0; f0];           % Define initial conditions.

tol = 1.e-3;		% Accuracy
trace = 1;
[t,y] = ode23('rabfox',t0,tfinal,y0,tol,trace);
plot(t,y), title('Rabbit and Foxes model time history'), pause

%  now plot Phase Portrait
plot(y(:,1),y(:,2),y0(1),y0(2),'+',[y(1,1) y(2,1)],[y(1,2) y(2,2)]), ...
title('Rabbit and Foxes - phase plane plot'),...
xlabel('Rabbit Population'), ylabel('Fox Population'),...
text(y0(1),y0(2),'Initial Populations'),pause