This homework involves setting up and analyzing a two-dimensional discrete dynamical system. We will start with some
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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.
Related Book For
Differential Equations and Linear Algebra
ISBN: 978-0131860612
2nd edition
Authors: Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. West
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