Long time behaviour of population models.

Abstract

Non-negative matrices arise naturally in population models. In this thesis, we look at the theory of such matrices and we study the Perron-Frobenius type theorems regarding their spectral properties. We use these theorems to investigate the asymptotic behaviour of solutions to continuous time problems arising in population biology. In particular, we provide a description of long-time behaviour of populations depending on the nature of the associated matrix. Finally, we describe a few applications to population biology.