%
% laglogis.m - this MATLAB file simulates the 
% lagged logistic difference equation
%  u(n+1)=a u(n) (1-u(n-1))
% as a system pof two first order equations:
% letting      x(n) = u(n-1)
%              y(n) = u(n)
% giving
%       x(n+1) = y(n)
%       y(n+1) = a*y(n)*(1-x(n)) 
% The user is prompted to read in the value
% of x0 and y0, the paramters a
% and the time interval over which to run the 
% simulation.
s=1;
while s>0;
a=input('input a=intrinsic growth rate:     ')
x0=input('input initial population at time 0:     ')
y0=input('input initial population at time 1:     ')
n=input('input time period of run:     ')
x=zeros(n+1,1);
y=zeros(n+1,1);
t=zeros(n+1,1);
equilibrium=(a-1)/a
x(1)=x0;
y(1)=y0;
for i=1:n
t(i)=i-1;
x(i+1)=y(i);
y(i+1)=a*y(i)*(1-x(i));
end
t(n+1)=n;
plot(t,x,t,x,'o')
title('time series'),pause
plot(x,y,x,y,'o')
title('semi-orbit'),pause
plot(x,y,'o')
title('semi-orbit not connected'),pause
s=input('Do you want to stop - if so enter 0')
end