kk=4000;
y=zeros(1,4000);
y(1)=0.5678;
figure('Position',[50,50,800,500]);
p=plot(2.8,-3.0,'EraseMode','none', 'Color', 'red');
xlim([2.80,4.00]);
ylim([-3.00,1.00]);
xlabel('r-value','FontSize',12);
ylabel('Lyapunov Exponent','FontSize',12);
title('Logistic Map','FontSize',12);
for r=2.8000:0.0001:3.9999;
 for j=2:kk;
  y(j)=r*y(j-1)*(1-y(j-1));
 end
 x=y(2001:4000);
 term=log(abs(r*(1.0-2.0*x)));
 total=sum(term)/length(term);
 set(p,'XData',r,'YData',total);
 drawnow;
end
hold on;
plot([2.8,4.0],[0.0,0.0],'-b','EraseMode','none');
hold off;