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Applications of Differential Equations

Population Dynamics

(continued from last page...)

You should now have:

Show[uscensusplot, malthusplot, verhulstplot]

Comparison Plot

What do you think? Which model did the better job of describing the data? Neither model is perfect:

  • The Malthusian model is too low almost the entire time, but looks like it's going to overshoot by quite a bit if we extrapolate it.
  • The Verhulst model fits the early data well, and the last point, but seems to overestimate in the latter half of the data.

Notice how both models fit the first and last points well. Is this surprising? After all, these were the points we used in calculating our parameters. One measure of a good model is to see how well it predicts the future. Go ahead and evaluate both malthus and verhulst for the year 2050.

Let's go look at what you should have gotten...


Compass If you're lost, impatient, want an overview of this laboratory assignment, or maybe even all three, you can click on the compass button on the left to go to the table of contents for this laboratory assignment.
 
 

ODE Laboratories: A Sabbatical Project by Christopher A. Barker

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