Similarity of General Population Matrices and Pseudo-Leslie Matrices

Authors

Jo?o F. Alves, Center of Mathematical Analysis, Geometry and Dynamical Sistems, Departamento de Matem´atica, Instituto Superior T´ecnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisbon, PortugalFollow
Henrique M. Oliveira, Center of Mathematical Analysis, Geometry and Dynamical Sistems, Departamento de Matem´atica, Instituto Superior T´ecnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisbon, PortugalFollow

Author Country (or Countries)

Portugal

Abstract

A similarity transformation is obtained between general population matrices models of the Usher or Lefkovitch types and a simpler model, the pseudo-Leslie model. The pseudo Leslie model is a matrix that can be decomposed in a row matrix, which is not necessarily non-negative and a subdiagonal positive matrix. This technique has computational advantages, since the solutions of the iterative problem using Leslie matrices are readily obtained . In the case of two age structured population models, one Lefkovitch and another Leslie, the Kolmogorov-Sinai entropies are different, despite the same growth ratio of both models. We prove that Markov matrices associated to similar population matrices are similar.

Recommended Citation

F. Alves, Jo?o and M. Oliveira, Henrique (2023) "Similarity of General Population Matrices and Pseudo-Leslie Matrices," Applied Mathematics & Information Sciences: Vol. 09: Iss. 5, Article 4.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss5/4