Consider the Leslic population model described in class where a population is divided in n age-...

Transcribed Image Text:

Consider the Leslic population model described in class where a population is divided in n age- classes (ordered so that i = 1 are newborns and in are elderly) and (k) denotes the number of individuals in age-class i at time k. At every time period k each of the zi (k) individuals produces a, offsprings (a, 20 fertility rate) progress to the next age class with survival rate € [0.1] leading to the dynamics 2₁(k+1) x2(k+1) x(k+1) = x3(k+1) an(k+1) = 01 CX2 *** an-1 CX₂ B₁ 0 0 0 0 0 0 3₁-1 0 Leslie matrix 1 x₂(k) x3(k) = Ax(k) ⠀ Assume that o, 20 and 12 8 20 for all i. 1. Find necessary and sufficient conditions on a.; so that the Leslie matrix is irreducible. (2p) 2. For an irreducible matrix as in the previous point find a sufficient condition on the parameters ₁, 3, that ensures that the population will not get extinct. (1p) Consider the Leslic population model described in class where a population is divided in n age- classes (ordered so that i = 1 are newborns and in are elderly) and (k) denotes the number of individuals in age-class i at time k. At every time period k each of the zi (k) individuals produces a, offsprings (a, 20 fertility rate) progress to the next age class with survival rate € [0.1] leading to the dynamics 2₁(k+1) x2(k+1) x(k+1) = x3(k+1) an(k+1) = 01 CX2 *** an-1 CX₂ B₁ 0 0 0 0 0 0 3₁-1 0 Leslie matrix 1 x₂(k) x3(k) = Ax(k) ⠀ Assume that o, 20 and 12 8 20 for all i. 1. Find necessary and sufficient conditions on a.; so that the Leslie matrix is irreducible. (2p) 2. For an irreducible matrix as in the previous point find a sufficient condition on the parameters ₁, 3, that ensures that the population will not get extinct. (1p)

Answer rating: 100% (QA)

1 Solution let 2 K1 Xn K1 Assume that Xizo and 1 Bizo K Sm This The ... View the full answer