Question: 2. Consider the predator-prey system, where an and yn are the population fractions of monkeys and tigers, respectively, beyond their environmental capacities. In this

2. Consider the predator-prey system, where an and yn are the population

2. Consider the predator-prey system, where an and yn are the population fractions of monkeys and tigers, respectively, beyond their environmental capacities. In this particular system, the interplay between the two species is given by the difference equations In+1 = In Yn, Yn+1 = 2n -Yn- (a) Letting Vn = (In, Yn) be the vector for the species at the nth generation, express the above equations in terms of a single matrix equation Vn+1 = Avn. (b) What are the eigenvalues of the matrix A? (c) Given these eigenvalues, what are the general solutions of an and yn? (Hint: lim tan-(x) = /2) 84X (d) Lastly, what can we infer about the long-term behavior of these populations?

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