## Mathematics & Science
Learning Center |
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## Applications of Systems of Differential Equations## Predator-Prey Problems
## The Effect of the Initial ConditionsThe next part of our investigation answers the question: What happens to the above graph if the initial conditions are changed? In fact, we will now do a series of problems in which we repeatedly generate
graphs similar to the one we just made, but we keep changing one little aspect
of the problem between plots—the The next problem, then, is as follows: Produce the rabbit-fox graph of the Lotka-Volterra model:
(Note that the only change here from our original problem is a new set of
initial conditions.) Plot it on the interval 0 ≤ Now where should we start? Well, by looking back at what we did last time might be a good idea! However, some of the work we did before is no longer required. In this new problem we are only asked for a single picture, the rabbits versus foxes graph. This is the parametrically generated plot that we did in the very last step. The individual plots of rabbits versus time and foxes versus time are not requested here. That's fine by us, right? Less work! So let's condense the steps required to make our picture down to the bare essentials. The following pair of commands should be sufficient:
rabfox2= Switch to Now let's go 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 |