% Logistic.m
% Author: Adolfo J. Rumbos
% This program  allows the user to input initial condition for a logistic 
% differnce equation.  It also allows for the input of the intrinsic growth
% rate.  The carrying capacity is assumed to be K=1.  The program can also 
% iterate the equation for as many generations as desired.  
% 
%
disp(' ')
disp('This program finds and plots solutions to the logistic difference equation')
disp(' ')
disp('                       N_{t+1} = N_t + r*N_t*(1-N_t)')
disp(' ')
disp(' ')
disp('Enter the intrinsic growth rate "r"')
r=input ('r = ');
%
disp(' ')
disp('Enter the initial population value "N_0"')
N_0=input ('N_0 = ');
%
disp(' ')
disp('Enter the number of generations:'); 
gen=input('(Default is 20)   ');
if isempty(gen) gen=20; end;
%
p=N_0; 
N=p;
for i=1:gen; p = p + r*p*(1 - p); 
N=[N p]; end
%
% Plotting routine
plot([0:gen], N, 'k-*')
y_max = max([N_0 N]) + 0.1;
axis([0 gen 0 y_max]); grid on;
title(['Logistic model with r = ', num2str(r), ', K=1, ', 'and ', 'N\_0 = ', num2str(N_0)])
xlabel('Time t');
ylabel('Population N');