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 x 0 y 0 1 5 1 4 3 1 2 2 x 1 y 1 1 22 5 02 1 212 4 056 3 444 1 052 2 352 2 076 x 2 y 2 1 483227 5 043494 1 464348 4 113952 3 924562 1 108025 2 750824 2 156233 x 3 y 3 1 795719 5 071223 1 762525 4 174501 4 436219 1 168543 3 197099 2 241277 x 4 y 4 2 163222 5 104037 2 111762 4 238392 4 971333 1 234051 3 689415 2 33177 x 5 y 5 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 Use the method of least squares to compute the values of the coefficients Find all of the fixed points of the system Determine the stability of each 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

Question: 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

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

Use the method of least squares to compute the values of the coefficients .
Find all of the fixed points of the system. Determine the stability of each.
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.

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To fit the discrete dynamical system to the data we can use the method of least squares This involves minimizing the sum of the squared errors between the model predictions and the actual data To do t... View full answer

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