For this assignment you will be reading the paper by Motesharrei, Rivas, and Kalnay and reproducing a few of their test cases. (Here is the link to the paper https://shared.com/dyhx2haa4x?s=l ).

This paper is centered around some results obtained from the Human and Nature Dynamics (HANDY) model. This model is equation 3 in their paper. The parameters CC and CE are given in equation 4, which relies on the wealth threshold wth from equation 5. Equation 6 provides the death rates for commoners and elites ( aC and aE). Other parameters found in these equations are free to be varied. Typical values for these parameters are given in the first table in Section 5. Your job is to reproduce the results in figures 3 and 4 from this paper.

The first step is to get the model working using ode45. If you recall the discussion in class you need to give ode45 a function to solve. In our case the function to be solved with by a user defined function (a function created by YOU) which solved the equations in the HANDY model. I found in my testing that it was sometimes necessary to play with the solver parameters used by ode45 by first calling odeset() and setting the RelTol to 10^4, and possibly setting all parameters to be stay positive with the NonNegative parameter. See help odeset for explanation on how to do this.

Once your model is up and running you'll then need to run ode45 on the parameter sets used for each simulation in figures 3 and 4. It will be necessary to plot using multiple axis because of the disparate scales in different solution parameters. Populations can run into the thousands, while nature shouldn't go over 100 "eco-Dollars". For help on making multiple Y axis on the same gure see http://www.mathworks. com/help/matlab/creating_plots/using-multiple-x-and-y-axes.html. It may be convenient to put all of the necessary instructions for plotting this way in a sub-function, and then calling that sub function for each set of solution data to be plotted.