bernoulli.m

Chaotic maps. Matlab simulation.

%THIS PROGRAM IS WRITTEN FOR BERNOULLI MAP FOR GENERATING RANDOM SEQUENCES
%WHICH EXHIBIT GOOD AUTOCORRELATION PROPERTIES MAKING A CALL FOR USAGE IN
%ENGINEERING APPLICATIONS.
clc;  close all;  clear all;

B = 1.75;  A = .5;  phin = 0.25;  phi(1) = (B*phin) - A;
for ii = 2:1:3000        
if phi(ii-1) > 0        
phi(ii) = (B*phi(ii-1)) - A;            
else      
phi(ii) = (B*phi(ii-1)) + A;        
end
end

%++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Bb = 1.99;  Aa = .35;  phint = 0.25;  phit(1) = (B*phint) - Aa;
%++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
for ni = 2:1:3000        
if phit(ni-1) > 0        
phit(ni) = (Bb*phit(ni-1)) - Aa;            
else      
phit(ni) = (Bb*phit(ni-1)) + Aa;        
end
end

CST = xcorr(phit,phi);  AST = xcorr(phi,phi);

for tt = 1:1:length(phi)-2    
    XX(tt) =  phi(tt+2);
    YY(tt) =  phi(tt+1);
    ZZ(tt) =  phi(tt);    
end
Time = 0;
for nn = 2:1:length(CST)
Time(nn) = Time(nn-1) + 1; 
end

figure(1);  plot(phi);             title('\bf Bernoulli MAP');       xlabel('\bf Time scale');   ylabel('\bf Amplitude fluctuations');
figure(2);  plot(ZZ,YY,'k.');      title('\bf Mapping');             xlabel('\bf X(n)');          ylabel('\bf X(n+1)');
figure(3);  plot(Time,AST,'r',Time,CST,'g');       title('\bf AUTO & CROSS correlation');    
xlabel('\bf Time');    ylabel('\bf Auto & Cross correlation'); legend('red-AC','green-CC');
figure(5);  plot3(ZZ,YY,XX,'r.');  title('\bf Pseudo phase space trajectories');  grid on;
xlabel('\bf X(n)');   ylabel('\bf X(n+1)');    zlabel('\bf X(n+2)');