AMATH 563 Homework 2 Dynamics and Model Discovery solved

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Consider the following historical (and classic) data set concerning Canadian lynx and snowshoe hare populations from 1845 to 1903.
Figure 1: Population data.
1. Develop a DMD model to forecast the future population states
2. Do a time-delay DMD model to produce a forecast and compare with regular DMD. Determine if it is
likely that there are latent variables.

3. Empirical Predator-Prey models such as Lotka-Volterra are commonly used to models such phenomenon.
Consider the model x˙ = (b − py)x and y˙ = (rx − d)y. Use the data to fit values of b, p, r and d.
4. Find the best fit nonlinear, dynamical systems model to the data using sparse regression.
5. Compute the KL divergence of the best model fit to the data between all the above models.
6. Retain three of your best fit models and compare their AIC and BIC scores.

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: download from the course website (It is next to HW 2)
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

pcolor(A), shading interp, pause(0.2)

This is an exploratory homework. So play around with the data and make sure to make lots of plots. Good
luck, and have fun.