AMATH 563
Homework 2: Model Discovery
Consider the following historical (and classic) data set concerning Canadian lynx and snowshoe hare populations from 1845 to 1903.
Figure 1: Population data.
1. Find the best fit nonlinear, dynamical systems model to the data using sparse regression.
2. Compute the KL divergence of the best model fit to the data.
3. Retain three of your best fit models and compare their AIC and BIC scores.
4. Time-delay embed the system and determine if there are latent variables.
Download the data set BZ.mat (which is a snipet from a Belousov-Zhabotinsky chemical oscillator movie –
check them out on youtube).
1. get the data: courses.washington.edu/amath582/BZ.mat
2. See what you can do with the data (i.e. repeat the first two steps above)
The following code may be helpful for view the data.
[m,n,k]=size(BZ_tensor); % x vs y vs time data
for j=1:k
A=BZ_tensor(:,:,j);
pcolor(A), shading interp, pause(0.2)
end
This is an exploratory homework. So play around with the data and make sure to make lots of plots. Good
luck, and have fun.
