linear_beetle.m equations 1.5 (page 39) of text. You can download this file by right clicking on the link and using the "save as ..." option

Output from linear_beetle.m [PNG format]

Sample writeup [Microsoft Word format]

Sample writeup [PDF format]

cobweb.m Generate cobweb plot

f.m sample function

Execute by typing

cobweb(@f,0,1,0.1,0.15);into matlab command window.

Codes for 2-body problem

Essential pieces for calculating correlation dimension:

N = length of data set "data", "r" is the tolerance, k is the number of data within the tolerance

for (i=1:N) for (j=1:N) if ((i ~= j) && (abs(data(i)-data(j)) < r)) k=1+k; end end endNote: This actually

for (i=1:N) for (j=i:N) % eliminate double counting ... if ((i ~= j) && (abs(data(i)-data(j)) < r)) k=1+k; end end endNow return k/N^2 (percentage of total points within tolerance r). The exact percentage is k/(N*(N-1)/2), but this introduces an additive constant of log(2) which dissapears in the limit...

To calculate correlation dimension (via least squares), use the Matlab built in function "polyfit", where the independent variable is log(r) and the dependent variable is log(C(r))