Help me with an equation please!!! (1 Viewer)

[kfnmpah]

Hey everyone, I have a question for my mathematical modelling assignment, it's the last question in the assignment and I have no idea how to do it.

Determine the equilibria of the solution analytically. What popu- lations of owls and mice are in equilibrium? From your numerical investigations, do you think these are stable equilibria?

The equations:

M(n+1) = 1.2M(n) − 0.001O(n)M(n)
O(n+1) = 0.7O(n) + 0.002O(n)M(n)

Where M(n) is the mouse population in year n and O(n) is the owl population.

Is it something to do with differential equations? Help!

Millions of cyber love to anyone that helps. (that's right, millions of cyber love /strong grammar)

 

[DeltaZero]

To find the equilibrium state, we can let n approach infinity so that the difference between M(n+1) and M(n) (similarly with O) approaches zero. Doing so we arrive at the equations:

M = 1.2*M - 0.001*O*M
O = 0.7*O + 0.002*O*M

Where M = M(n+1) = M(n) as n approaches infinity (similarly with O)

I'm not going to solve it, you can do that, but it should net you the equilibrium solution.