# 7 a suppose two populations of animals follow the

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Unformatted text preview: such that if g1 = αf1 + β f2 and g2 = γ f1 + δ f2 ￿ ￿T ￿ ￿ ￿1 α γ then 0 g1 g2 = . β δ 7. (a) Suppose two populations of animals follow the discrete dynamical system p(t + 1) = 1.7p(t) − .6q (t) q (t + 1) = −.6p(t) + .8q (t). You are told that the eigenvalues of the relevant matrix are 2 and 1 . Determine p(t) and q (t) in the case where p(0) = 100 and 2 q (0) = 200. (b) Solve the system of diﬀerential equations ￿ ￿ 1.7 −0.6 ￿ ￿= x ￿ x −0.6 0.8 ￿￿ 100 when x(0) = . 200 8. Determine the steady-state behavior of the Markov chain with transition matrix given by the Markov matrix 0.3 0.2 0.7 0.4 0.5 0.2 . 0.3 0.3 0.1...
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## This note was uploaded on 01/30/2014 for the course MATH 2940 taught by Professor Hui during the Fall '05 term at Cornell University (Engineering School).

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