Persistence and global asymptotic stability of single species dispersal models with stage structure

Abstract

A system of retarded functional differential equations is proposed as a model of single-species population growth with dispersal in a multi-patch environment where individual members of the population have a life history that takes them through two stages, immature and mature. The persistence of the system as well as the existence and global asymptotic stability of a positive equilibrium is proved by using the monotone dynamical systems theory due to Hirsch and Smith, and a convergence theorem established in this paper for nonautonomous retarded equations by using limiting equations theory.