% Compute the Lyapunov exponent of the
% Logistic map for alpha=[2.4,4].

x0 = 0.5;
alpha=[2.4:0.001:4];           
OutLog = 200; % 100< - <300     
OutLyap = 7000;  % 500< - <10000  
for i=1:size(alpha,2)   
    x = x0;
    alpha(i);
    for j=1:OutLog     
        x = alpha(i)*x*(1-x);
    end
    sum(i) = 0;         
    for j=1:OutLyap
        x = alpha(i)*x*(1-x);
        sum(i) = sum(i) + log(abs(alpha(i)-2*alpha(i)*x));
    end
    sum(i) = sum(i)/OutLyap; 
end

LL=length(alpha);
zero=zeros(1,LL);

figure; 
text(2.6,.65,...
    texlabel('lambda>0: Chaotic')); 
hold on;
text(2.6,.5,...
    texlabel('lambda(x_0)=(1/n) lim [ Sigma_0^(n-1)log|f^,(x_i)| ]'));
hold on;
text(2.6,-0.7,...
    texlabel('lambda<0: Deterministic '));
plot(alpha,sum,'b',alpha,zero,'r');
title('Lyapunov exponent of Logistic map');
xlabel(' 2.5 \leq \alpha \leq 4');
ylabel('Lce')
axis([2.5 4 -1.2 0.8]);
grid;


% "Complex and Chaotic Nonlinear Dynamics. 
% Advances in Economics and Finance, 
% Mathematics and Statistics" 
% T.Vialar, Springer 2009.
% Copyright(c).