% logistics map - Strogatz
% Math 553 - DeLillo, Fall 2011
N = 40;  % number of iterations
xn(1:N)=zeros(1,N);  % initialize interation vector
xc(1:2*(N-1))= zeros(1,2*(N-1));  % initialize vector for cobweb plot
xn(1)=.9;  % initial guess
r = 3.449;  % fix value of r
for n=1:N-1
  xn(n+1) = r*xn(n)*(1-xn(n)); 
end

% Plot output

figure(1) % time series generated by f = r*x*(1-x)
plot(1:N,xn,'-o')

figure(2); % plot of map f from time series
plot(xn(1:N-1),xn(2:N),'o');
axis([0 1 0 1]);

figure(3); % cobweb plot
xc(1:2:2*(N-1))=xn(1:N-1);
xc(2:2:2*(N-1))=xn(1:N-1);   
xc2(1:2:2*(N-1)-1)=xn(1:N-1);
xc2(2:2:2*(N-1))=xn(2:N);
xp=(0:100)/100;
plot(xc,xc2,'-o',xp,r*xp.*(1-xp),xp,xp)
