## Mathematics & Science
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## Applications of Differential Equations## Population Dynamics
You probably remember that when we solved the Verhulst model's differential equation we included an initial condition. The resulting solution contained two parameters and was an incredible mess! We're not going to use that messy version of the solution this time, and we're not even going to need the initial condition, as we'll use something else instead, (more on that later.) usverhulstfit = l/(1 + E^(-k (t - 1990))) This is basically the version of the model you will find in Wikipedia if you were to look it up there. (The numerator here is a lowercase L, though it may look like a one in your browser.) Admittedly this is still not pretty, but it is definitely better. You may be wondering where the 1990 came from in the equation. This should be the Next we'll see if FindFit can find the unknown parameters without us giving it any help (like we had to with Malthus.) Enter the command: FindFit[uscensus, usverhulstfit, {l, k}, t] Let's move on and see what you should have gotten... |
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ODE Laboratories: A Sabbatical Project by Christopher A. Barker©2017 San Joaquin Delta College, 5151 Pacific Ave., Stockton, CA 95207, USA e-mail: cbarker@deltacollege.edu |