Differential Equations Calculus II Assignment Question

[llg2124]

Hi, need to complete this written assignment for my Calculus II class and am not sure that I am formatting it correctly...any help would be much appreciated!

In the wilds of Canada, the common beaver is the main predator of the moose.When moose are plentiful, beavers thrive and their population increases; when moose become scarce, beaver population begins to decline a week later. Conversely, when the woods are thick with beavers, moose population dwindles, but when the beavers vanish, the moose repopulate. Let B be the number of beavers in Ontario, M the number of moose. Write a plausible pair of differential equations satised by M and B respectively (with respect to time) that would reproduce the above behaviour. Define all your variables, and (briefly!) explain why your equation works.

I thought that B=constant1(dM/dt) and M=constant2(1/(dB/dt)), but I am not sure how to write these equations in terms of time, whether I should combine them into one equation, and how to do that.

Thanks so much!!

 

[HallsofIvy]

Beavers are predators on Moose? What do they do, gnaw on the moose's feet?

First, dM/dt is the rate at which the moose population increases (positive) or decreases (negative). The moose population can't increase without having male and female moose! That is, dM/dt must depend on the number of mooses, M. Yes, it will also decrease because of the beaver population, B. So we must have dM/dt= aM- bB where both a and b are positive. Similarly for dB/dt.

(This is a simple model. One could also argue the increase in the moose population requires that a (male) moose meet a (female) moose and that is proportional to \(\displaystyle M*M= M^2\) and similarly for the beavers so that we would have \(\displaystyle dM/dt= aM^2- bB\) and \(\displaystyle dB/dt= cB^2- dM\).)