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

Y Kyrychko, SA Gourley, MV Bartuccelli

Research output: Contribution to journalArticle (Academic Journal)peer-review

10 Citations (Scopus)

Abstract

We study a nonlocal time-delayed reaction-diffusion population model on an infinite 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.
Translated title of the contributionComparison and convergence to equilibrium in a nonlocal delayed reaction-diffusion model on an infinite domain
Original languageEnglish
Pages (from-to)1015 - 1026
Number of pages12
JournalDiscrete and Continuous Dynamical Systems- Series B
Volume5 (4)
Publication statusPublished - Nov 2005

Bibliographical note

Publisher: American Institute of Mathematical Sciences

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