This homework involves setting up and analyzing a two-dimensional discrete dynamical system. We will start with some data and a model form:

Suppose that we look at four initial conditions, and for each, we record the values of through:

x0	y0	1	5	1	4	3	1	2	2
x1	y1	1.22	5.02	1.212	4.056	3.444	1.052	2.352	2.076
x2	y2	1.483227	5.043494	1.464348	4.113952	3.924562	1.108025	2.750824	2.156233
x3	y3	1.795719	5.071223	1.762525	4.174501	4.436219	1.168543	3.197099	2.241277
x4	y4	2.163222	5.104037	2.111762	4.238392	4.971333	1.234051	3.689415	2.33177
x5	y5	2.590605	5.142891	2.516527	4.306474	5.520396	1.305065	4.223885	2.428399

We want to fit this data to a discrete dynamical system of the form

1. Use the method of least squares to compute the values of the coefficients .
2. Find all of the fixed points of the system. Determine the stability of each.
3. Sketch the overall behavior of the system. (This can be a hand-drawn image, one constructed using a drawing tool, a plot constructed in Excel from data points.