Question

In: Advanced Math

Given is a population of wolves (W) and rabbits (R). R[t+1] = R[t]+ g*R[t] * (1...

Given is a population of wolves (W) and rabbits (R). R[t+1] = R[t]+ g*R[t] * (1 – R[t]/K) - sR[t]W[t] W[t+1] = (1-u)W[t] + vR[t]W[t] Where the carrying capacity of rabbits is 1 million. The growth rate of rabbits is 10% a year and s is equal to 0.00001, v is 0.0000001, and u is equal to 0.01. How many wolves and how many rabbits exist in the equilibrium?

Solutions

Expert Solution

Answer:)

Inputting the givens in the equation, we get the following:

Suppose that the equilibrium value of the Wolf population and the Rabbit Population is W and R respectively, we will have that, at equilibrium :

Which simplifies down to:

For both these equations to hold simultaneously, we must have the following possibilities:

  • From the first equation, R = 0 which immediately gives from the second equation, that W = 0.
  • W = 0 and R = 1000000, from the second and first equation respectively.
  • from the second equation and

The equilibrium condition is then the case when (R,W) = (100000,9000) since the others are special cases of no rabbits or wolves, or an overabundance of rabbits and no wolves.

Colby Messinger answered 2 years ago
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