## Applications of Systems of Differential Equations

### Predator-Prey Problems

(continued from last page...)

### Exercises

In each of the following exercises the instructions are the same:

Produce the rabbit-fox graph of each Lotka-Volterra model given, on the interval 0 ≤ t ≤ 10. Read the solution into the variable rabfox#, and the plot itself into the variable rabfoxplot#, where # represents the number of the exercise you are doing, i.e. either 3, 4, 5, or 6. (We already did 1 and 2 while I was helping you.

When you have finished creating the required graph for each exercise you should click on the "Check Answer" button to check your answer for accuracy.

EXERCISE 3
System Initial Conditions Check
r′(t) = 2 r(t) - 0.01 r(t) f(t)
f′(t) = - f(t) + 0.01 r(t) f(t)
r(0) = 120
f(0) = 200

EXERCISE 4
System Initial Conditions Check
r′(t) = 2 r(t) - 0.01 r(t) f(t)
f′(t) = - f(t) + 0.01 r(t) f(t)
r(0) = 100
f(0) = 200

Note: this graph should be a single point! (It may be hard to see. It's coordinates are (100, 200).) What does this single point graph mean as far as the dynamics of the two populations are concerned? What would the graphs of rabbits vs. time, and foxes vs. time look like?

EXERCISE 5
System Initial Conditions Check
r′(t) = 2 r(t) - 0.01 r(t) f(t)
f′(t) = - f(t) + 0.01 r(t) f(t)
r(0) = 400
f(0) = 100

EXERCISE 6
System Initial Conditions Check
r′(t) = 2 r(t) - 0.01 r(t) f(t)
f′(t) = - f(t) + 0.01 r(t) f(t)
r(0) = 800
f(0) = 20

Note: In this case Mathematica will not form a complete orbit unless you include the PlotRange->All option, so make sure you do!

To finish off this laboratory, we're going to make one last picture...

 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

©2017 San Joaquin Delta College, 5151 Pacific Ave., Stockton, CA 95207, USA
e-mail:
cbarker@deltacollege.edu