Global dynamics and Hopf bifurcation of a structured population model

Abstract

In this paper, we consider a system of delay differential equations which describes a structured single species population distributed over a two-patch environment. For a large class of birth functions, we obtain sufficient conditions for uniform persistence and global stabilities of equilibria. A Hopf bifurcation in this system is also discussed when the birth function takes a specific form, and the stability of the bifurcated periodic solutions and the bifurcation direction are investigated in detail. Finally, some numerical simulations of the system are given. © 2004 Elsevier Ltd. All rights reserved.