GS 2000/Math - Collins
Lab 5
Data for Chaos

In this lab we will use be collecting data from a nonlinear
difference equation to understand chaos.


Nonlinear Difference Equation

   Solve x(n+1) = a x(n) (1-x(n)) for various values of a and x(0)

   Write a MATLAB script (or function) which lets the user input
   a and x(0), computes x(1), ..., x(100) and 
   then prints out the following values (on one line)

      a    x(96) x(97) x(98) x(99) x(100) 

   Run with 10 different values of a (between 0 and 4) and
   for each value of a use 5 different starting values x(0),
   (between 0 and 1).

   Save the 50 lines of output (copy and paste them into a file or mail
   message) and mail them to me at 
       ccollins@math.utk.edu

 
 

Sample Script


% script file to simulate the difference equation x(n+1) = a x(n)(1-x(n)) 

a = input('Enter the value for a:');
x(1) = input('Enter the initial value (x(0)):');

for n = 1:100
   x(n+1) = a*x(n)*(1-x(n)); 
end

plot(x)
disp([a x(96:100)])

% end of script


ccollins@math.utk.edu
Last Modified: June 26, 2000