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% Math 3520: Differential Equations and Dynamical Systems
%  Compute and plot the orbit diagram for logistic maps. 
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%% Logistic map function with parameter r,  0<r<4
lrx = @(r,x) r*x.*(1-x);  % use componentwise ".*"

rmin = 3.0;  rmax = 3.5;  % range of parameter values
dr = 0.01;                 % parameter increment
x0 = 0.5;                 % initial value for iteration

figure; hold on;   % New graph, accumulate points
plot(rmin,0,"."); plot(rmax,1,".");  % plot limits

for(r=rmin:dr:rmax)   % increment over parameter range
 % Iterate with a given r, always starting with x0
 x = x0;
 for(i=1:300) x=lrx(r,x); end  % transient portion
 for(i=301:600)                % orbit portion
   x = lrx(r,x);
   plot(r,x,".");
 end
end
title("Orbit Diagram for Logistic Map Iteration");
xlabel("r, in r*x*(1-x)"); ylabel("Orbit points");