Consider a forest that contains Foxes and Wolves which compete for the same food

Question

Consider a forest that contains Foxes and Wolves which compete for the same food resources. If Fn and Wn represent the populations of foxes and wolves, respectively, at the end of month n, a model for their populations is: Fn+1 = 1.2 Fn 0.001 FnWn and Wn+1 = 1.3Wn 0.002 FnWn

(a) Explain the meaning of the parameters 1.2 and 1.3.

(b) Why are the parameters -0.001 and -0.002 both negative?

(c) Find the equilibria for this system and graphically determine if they are stable or unstable (consider only up to n = 25).

(d) Is this model sensitive to the initial populations? Why or why not?

Explanation / Answer

a)1.2 and 1.3 , we can say are reproduction ratio.

b) they both are negative since they both are competing for the same food sources.

c)

d) its not sensitive to initial population it will converge to

0.2 = 0.001 Wn

W_n = 200

0.3 = 0.002 F_n

150 = F_n

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