% coded by K. Stewart, reference Kahaner, Moler and Nash, p. 332
% (P8-5) in exercises for statement of problem
%
clear
echo off
clc

%	Consider rabbits and foxes
%	   r'(t) = 2*r - alf * r * f
%	   f'(t) = -f + alf * 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 parameter alfa with the derivative routine
global alfa


t0 = 0;
tfinal=input('enter final value of time (e.g. 10) ');
% a column vector
y0 = [r0 f0]';		% Define initial conditions.

% [t,y] = ode23('rabfox',t0,tfinal,y0);

pause	% Strike any key to start ODE23 solution.

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

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'),...
text(y0(1),y0(2),'Initial Populations'),pause