[Matlab] Correlation function for henon map

[cadi2108]

Hi!

I need to write MATLAB script, which will be plotting corretation function for two-dimmensial system. Henon map is not my system, but is very popular, so solusion for henon map can be very helpful for me.

Have anybody know code for have plot like this: http://www.physics.emory.edu/~weeks/research/time/tseries6/autohen.gif? I wrote resolusion like it for logistic map, but it give me other type of plot:

clear;

n1=400; %% no of lattice points in coordinate and parameter k1
n2=200; %% no of iterations to reach attractor
n3=400; %% no of iterations for bifurcation diagram
n4=5000; %% no of iterations for distribution and Lyapunov exponent

kk=[]; w1=[]; 

k1=3.7; 
x1=0.1; 
                  
for it1=1:n2 
  y1=k1*x1*(1-x1); x1=y1;
end 

for iter3=1:n4  
  y1=k1*x1*(1-x1); w1=[w1;y1]; x1=y1;
end 

ww=.005 + linspace(0,.99,100);

w3=round(w1);
av1=mean(w3); % > the average 
var1 = cov(w3); % > the variance
var2=var1;
ww=w3;

for iter4=1:n2
  ww=[ww(n4);ww(1:n4-1)];
  zz=cov(w3,ww);
  var2=[var2;zz];
end 

var2=var2/var1;

bar(var2);
title('Autocorrelation function for the symbolic sequence'); 
axis([0  n2  -1  1]);

Help please! Best regards.

 

[mark726]

Hi there!

There are a few different ways you could approach this problem, but I'll outline one possible solution using MATLAB. The first step is to define the Henon map function, which takes in the current x and y values and returns the next x and y values based on the Henon map equations:

function [x_next, y_next] = henon(x, y, a, b)
x_next = 1 - a*x^2 + y;
y_next = b*x;
end

Next, we can define the parameters and initial conditions for our system:

a = 1.4; % parameter a for Henon map
b = 0.3; % parameter b for Henon map
x0 = 0.1; % initial x value
y0 = 0.1; % initial y value
n = 5000; % number of iterations to reach attractor
m = 400; % number of iterations for correlation function
x = zeros(n, 1); % preallocate arrays for x and y values
y = zeros(n, 1);

Now, we can run a loop to calculate the x and y values for each iteration and store them in the arrays:

for i = 1:n
[x(i+1), y(i+1)] = henon(x(i), y(i), a, b);
end

Now, we can plot the Henon map attractor by plotting the x and y values:

figure;
plot(x, y);
xlabel('x');
ylabel('y');
title('Henon Map Attractor');

To calculate the autocorrelation function, we can use the built-in MATLAB function "corrcoef". This function calculates the correlation coefficient between two variables, in this case the x and y values at different time lags. We can then plot these values as a function of the time lag using the "bar" function:

figure;
corr = zeros(m, 1); % preallocate array for correlation function
for j = 1:m
corr(j) = corrcoef(x(1:end-j), y(j+1:end)); % calculate correlation coefficient
end
bar(corr);
xlabel('Time lag');
ylabel('Correlation coefficient');
title('Autocorrelation Function for Henon Map');

I hope this helps! Let me know if you have any questions or if you need further clarification. Good luck with your project!