quadratic.asv

Chaotic maps. Matlab simulation.

%THIS PROGRAM IS WRITTEN FOR DEMONSTRATION OF QUADRATIC MAP (CHAOTIC MAP)
%AND ITS TRAJECTORY,2D MAPPING AND AUTOCORRELATION.
clc; close all; clear all;

A = 4;  B = .5;  phin = 0.15;  phi(1) = B - A*(phin^2);
for ib = 2:1:6000
phi(ib) = B - (A*(phi(ib-1).^2));    
end

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    

figure(1);   plot(phi);              title('\bf QUADRATIC map');    xlabel('\bf Time series');  ylabel('\bf Amplitude');
figure(2);   plot3(ZZ,YY,XX,'r.');   title('\bf Pseudo phase space trajectories');  grid on;
figure(3);   plot(ZZ,YY,'k.');       title('\bf Mapping');          xlabel('\bf X(n)');         ylabel('\bf X(n+1)');
figure(4);   plot(AST);       title('\bf Auto correlation'); xlabel('\bf Time');     ylabel('\bf correlation value');
xlabel();    ylabel();     zl
% vary B(bifurcation parameter) = .25 P1,.32 P2,.35 &.37 HIGHER periods,.38
% CHAOTIC OSCILLATIONS