% logist_stoch.m uses the Euler method to solve a stochastic logistic
% equation. Adapted from http://www-math.bgsu.edu/~zirbel/sde/
T=20;                     % maximum time to go to
h=0.1;                  % time step
N=ceil(T/h);             % number of steps to take
r=3.3;
K=1.4;
t=zeros(N,1);            % prepare a place to store times
z=zeros(N,1);            % prepare a place to store locations

t(1) = 0;                % initial time
z(1) = 1;                % initial location
for i=1:N                % take N steps
  t(i+1) = t(i) + h;
  z(i+1) = z(i)+(r+2*rand)*z(i)*(1-z(i)/(K+0.2*rand))*h;  
end;

%clf
figure
plot(t,z);          
axis([0 T (min(z)) (max(z)+1)]);   % set axis limits
title('Stochastic logistic growth');