University of Surrey

Test tubes in the lab Research in the ATI Dance Research

Linear and nonlinear stability in a diffusional ecotoxicological model with time delays

Schley, D. and Gourley, S. A. (2002) Linear and nonlinear stability in a diffusional ecotoxicological model with time delays Discrete and Continuous Dynamical Systems, 2. pp. 575-590.

[img]
Preview
PDF
fulltext.pdf

Download (418kB)

Abstract

We propose a reaction-diffusion extension of a two species ecotoxicological model with time-delays proposed by Chattopadhyay et al. (1997). Each species has the capacity to produce a substance toxic to its competitor, and a distributed time-delay is incorporated to model lags in the production of toxin. Additionally, nonlocal spatial effects are present because of the combination of delay and diffusion.

The stability of the various uniform equilibria of the model are studied by using linearised analysis, on an infinite spatial domain. It is shown that simple exponentially decaying delay kernels cannot destabilise the coexistence equilibrium state.

In the case of a finite spatial domain, with purely temporal delays, a nonlinear convergence result is proved using ideas of Lyapunov functionals together with invariant set theory. The result is also applicable to the purely temporal system studied by other investigators and, in fact, extends their results.

Item Type: Article
Additional Information: First published in Discrete and Continuous Dynamical Systems B, 2, 575-590. © 2002 American Institute of Mathematical Sciences.
Uncontrolled Keywords: non-local, ecotoxicological, competition, coexistence, stability, global convergence
Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:41
Last Modified: 23 Sep 2013 18:33
URI: http://epubs.surrey.ac.uk/id/eprint/1517

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year


Information about this web site

© The University of Surrey, Guildford, Surrey, GU2 7XH, United Kingdom.
+44 (0)1483 300800