## Mathematics & Science
Learning Center |
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## Applications of Systems of Differential Equations## Combat Models: Who Will Win The Battle?## Conventional Combat Model
In this model we have two conventional forces fighting against each other. A possible model for the situation might be this system of differential equations: b′(t) = -b(t) - 4 f(t) + 5
f ′(t) = -3b(t) - 2 f(t) + 5
b(0) = b_{o}, f(0)) = f_{o}
where
The British army's rate of change is dependent on three
terms: -
In executing your -
Use sensible naming conventions for your results. -
The values of *b*(*t*) and*f*(*t*) change*extremeley rapidly*in this model. Because of this, you may find that using an extremely short domain for*t*is prudent. I have suggested such domains next to each problem. -
Using the plotting option PlotRange->{{0,20},{0,20}} is helpful, giving you a view of the portion of the solution curve that is really relevant.
Which army, if any, wins under each of the following initial conditions, given in the form ( - (20, 20), using the interval 0 ≤
*t*≤ 4 - (21, 20), using the interval 0 ≤
*t*≤ 1 - (20, 21), using the interval 0 ≤
*t*≤ 1
Finish up your analysis by showing all three of your solution curves on the same plot by employing the Show command. If you're finished with the above analysis, you may go on to the next page for an overview of the results you should have found. |
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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 |