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Applications of Systems of Differential Equations

Predator-Prey Problems

(continued from last page...)

Your new foxes versus rabbits picture should look like this:

rabfoxplot1=ParametricPlot[{rab1,fox1},{t,0,10}]

Phase Plot

This graph illustrates an interesting relationship between the two populations. They form what is called a stable orbit in rabbit-fox space. Our initial condition was (300, 150), which lies at the bottom-right corner of the above plot, as shown by the red dot in the following picture. Looking back at our previous plots we know that both the rabbit and fox populations initially grow. This would imply that as time passes, the population mix moves counter-clockwise around the orbit. This movement with respect to time is indicated by the arrows in the following picture. (Note that I've also repositioned the axes so that they intersect at (0,0) in order for you to better visualize the orbit.)

Annotated Phase Plot

Once you have thoroughly considered the implications of the picture we can move on to do some further exercises...


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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