Mathematics & Science
Applications of Systems of Differential Equations
Combat Models: Who Will Win The Battle?
Mixed Combat Model
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In this model we have a guerilla force fighting against a conventional army. A possible model for this situation might be this system of differential equations:
c′(t) = -g(t)
g(0) = go, c(0) = co
where g(t) represents the guerilla force strength at time t, and c(t) represents the conventional force strength at time t, go is the initial guerilla strength, and co is the initial conventional force strength. All numbers are measured in thousands. Once again, carefully consider the relationships of the variables.
This time the combat loss rates of the two forces aren't symmetric with respect to one another. The guerilla combat loss rate is proportional to the number of guerilla-conventional encounters, whereas the conventional combat loss rate is proportional only to the number of guerillas. Think about their differing styles of warfare, and you might see why this should be so. Guerillas don't choose to fight a conventional force openly, but favor tactics such as ambush, and sneak raids on army bases.
Let's now move on to consider the most tradional situation...
ODE Laboratories: A Sabbatical Project by Christopher A. Barker
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