optimip.m

Chaotic maps. Matlab simulation.

% RECENTLY THERE HAS BEEN DEMONSTRATIONS OF BREAKAGE OF DIFFERENT CHAOTIC
% MAPS LIKE BERNOULLI and OTHER MAPS.SO HERE WE ARE GOING FOR NOVEL
% APPROACH IN THE SENSE OF MIXING VARIOUS MAPS IN DIFFERENT WAYS.HERE EVERY
% OTHER SAMPLE IS FROM DIFFERENT MAP.

clc;  close all;   clear all;

theta = 45;
z1 = 2; z2 = 3; z3 = 4;
X(1)  = sin(theta*pi*(z1^1))^2;
X1(1) = sin(theta*pi*(z2^1))^2;
X2(1) = sin(theta*pi*(z3^1))^2;

for ii = 2:1:6000
   X(ii) = sin(z1*asin(sqrt(X(ii-1))))^2;
   X1(ii) = sin(z2*asin(sqrt(X1(ii-1))))^2;
   X2(ii) = sin(z3*asin(sqrt(X2(ii-1))))^2;
end

for it = 1:1:length(X)-2
    Fi(it) = X(it+2);       Se(it)  = X(it+1);     Th(it)  = X(it);
    Fi2(it) = X1(it+2);     Se2(it) = X1(it+1);    Th2(it) = X1(it);
    Fi3(it) = X2(it+2);     Se3(it) = X2(it+1);    Th3(it) = X2(it);
end

kg = 1;
for lg = 1:1:2000    
    JS(kg)    = X(lg);
    JS(kg+1)  = X1(lg);
    JS(kg+2)  = X2(lg);    
    kg = kg + 3;
end

JJS = xcorr(JS,JS);

for mn = 1:1:length(JS)-2
    UTF(mn) = JS(mn+2);
    UTS(mn) = JS(mn+1);
    UTT(mn) = JS(mn);    
end
figure(1);   subplot(211);  plot(X);   title('\bf F R maps order 2'); subplot(212);   plot(Se,Fi,'m.');           
figure(2);   subplot(211);  plot(X1);  title('\bf F R maps order 3'); subplot(212);   plot(Se2,Fi2,'r.');         
figure(3);   subplot(211);  plot(X2);  title('\bf F R maps order 4'); subplot(212);   plot(Se3,Fi3,'k.');         
figure(4);   subplot(211);  plot(JS);  title('\bf F R maps order 5'); subplot(212);   plot(UTF,UTS,'r.');         
figure(5);   plot3(Th,Se,Fi,'r.');     title('\bf F R 3D'); xlabel('\bf X(n)');  ylabel('\bf X(n+1)');  zlabel('\bf X(n+2)');
figure(6);   plot3(Th2,Se2,Fi2,'r.');  title('\bf F R 3D'); xlabel('\bf X(n)');  ylabel('\bf X(n+1)');  zlabel('\bf X(n+2)');
figure(7);   plot3(Th3,Se3,Fi3,'r.');  title('\bf F R 3D'); xlabel('\bf X(n)');  ylabel('\bf X(n+1)');  zlabel('\bf X(n+2)');
figure(9);   plot3(UTT,UTS,UTF,'r.');  title('\bf F R 3D'); xlabel('\bf X(n)');  ylabel('\bf X(n+1)');  zlabel('\bf X(n+2)');
figure(10);  plot(JJS);                title('\bf A.C.Plot');