Table of Contents
ISRN Applied Mathematics
Volume 2012 (2012), Article ID 391547, 11 pages
http://dx.doi.org/10.5402/2012/391547
Research Article

A Mathematical Model of Three-Species Interactions in an Aquatic Habitat

Department of Mathematics, University of Jos, PMB 2084, Jos, Nigeria

Received 16 November 2011; Accepted 13 December 2011

Academic Editors: M. Mei and X. Meng

Copyright © 2012 J. N. Ndam et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A mathematical model for three-species interactions in a food chain, with the assumption that the interacting species are mobile, has been constructed using a combination of Holling’s type III and the BD functional responses. Conditions for the onset of diffusive instability were determined. The results indicate the possibility of a stable coexistence of the three interacting species in form of stable oscillations under the reflecting boundary conditions. Habitat segregation also occurs under these conditions. However, under the absorbing boundary conditions, the species experience damped oscillations leading to their extinction. The effects of cross-diffusion of the intermediate and the toppredator were also examined.