Comparison and convergence to equilibrium in a nonlocal delayed reaction-diffusion model on an infinite domain

Bartuccelli, Michele V, Gourley, S A and Kyrychko, Y (2005) Comparison and convergence to equilibrium in a nonlocal delayed reaction-diffusion model on an infinite domain. Discrete and Continuous Dynamical Systems - Series B, 5 (4). pp. 1015-1026. ISSN 1531-3492

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Abstract

We study a nonlocal time-delayed reaction-di®usion population model on an in¯nite one-dimensional spatial domain. Depending on the model parameters, a non-trivial uniform equilibrium state may exist. We prove a comparison theorem for our equation for the case when the birth function is monotone, and then we use this to establish nonlinear stability of the non-trivial uniform equilibrium state when it exists. A certain class of non-monotone birth functions relevant to certain species is also considered, namely birth functions that are increasing at low densities but decreasing at high densities. In this case we prove that solutions still converge to the non-trivial equilibrium, provided the birth function is increasing at the equilibrium level.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Yuliya Kyrychko
Date Deposited: 06 Feb 2012 21:05
Last Modified: 13 Jun 2012 13:26
URI: http://sro.sussex.ac.uk/id/eprint/29427
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