diffdem.m

Chaotic maps. Matlab simulation.

%THIS PROGRAM IS TO DEMONSRATE THE EXTREME SENSITIVITY OF CHAOTIC LOGISTIC
%MAP TO INITIAL CONDITION CHANGE IN BIFURCATION PARAMETER TO ORDER 10^-15
%SINCE MATLAB LOWER LIMIT IS (10^-15).same can be shown to any maps.

clc;   close all;  clear all;
format long g;

%--------------------------------------------------------------------------
% LOGISTIC MAP see B1 & BA1 difference 
%--------------------------------------------------------------------------
A1 = .5; B1 = 3.999999999; phin1 = -0.35;
phi1(1) = ( B1*[(A1^2) - (phin1^2)] ) - A1;
for ih = 2:1:300
  phi1(ih) = ( B1*[(A1^2) - (phi1(ih-1)^2)] ) - A1;  
end

% THIS IS SECOND CHAOTIC LOGISTIC MAP

AA1 = .5; BA1 = 3.999999998; phinA1 = -0.35;
phiA1(1) = ( BA1*[(AA1^2) - (phinA1^2)] ) - AA1;
Time = 0;
for ih = 2:1:300
  phiA1(ih) = ( BA1*[(AA1^2) - (phiA1(ih-1)^2)] ) - AA1;  
  Time(ih) = Time(ih-1) + 1;
end

%AUTO CORRELATION BETWEEN ABOVE TWO CHAOTIC MAPS WITH VERY MINUTE INITIAL
%VALUE DIFFERENCE OF 0.00001
Aff1 = xcorr(phi1);
Aff2 = xcorr(phiA1);
Dff = xcorr(phi1,phiA1);

figure(1);  
subplot(211);  plot(phi1);    title('\bf L map with initial value of 3.999999999');
subplot(212);  plot(phiA1);   title('\bf L map with initial value of 3.999999998');

figure(2);    
subplot(311);  plot(Time,phi1,'r',Time,phiA1,'g');   title('\bf difference B/W maps with inital difference of 1.0e-009');
subplot(312);  plot(Aff1,'r');                       title('\bf AUTO CORRELATION OF FIRST  MAP');
subplot(313);  plot(Aff2,'g');                       title('\bf AUTO CORRELATION OF SECOND MAP');

figure(3);    
subplot(211);   plot(phi1,phiA1,'r.'); title('\bf Synchronization between maps');
subplot(212);   plot(Dff,'g.');        title('\bf Cross Correlation between two');