Eigenvalues of the transition matrix

Reference no: EM13124289

A discrete dynamical system model for the population of cheetahs and gazelles in Namibia is given by the following pair of equations:

.3Ck + .4 Gk = Ck+1
-pCk + 1.3 Gk = Gk+1

where Ck measures the number of cheetahs present in a certain Namibian game reserve at time K, Gk gives the number of gazelles (measured in tens), and k is measured in months.

a) Find a value for p that guarantees a steady- state outcome for this model, then determine the number of cheetahs present for every 1000 gazelles (in the long run).

b) Find a value for p that will guarantee 2% growth in both populations. In the long-run, what is the ratio of gazelles to cheetahs?

c) What must be true about the eigenvalues of the transition matrix if both populations die out in the long- run?

Reference no: EM13124289

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