Advances in Theoretical and Applied Mathematics
ISSN 0973-4554 Volume 2 Number 2 (2007), pp. 103-116
© Research India Publications
http://www.ripublication.com/atam.htm
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A Two Species Competition Model with Diffusion and a Common Supplementary Resource in Two-Patch Habitat

Joydip Dhar
Department of Applied Mathematics,
ABV-Indian Institute of information Technology and Management,
Gwaliar-474 010, M.P, India
E-mail: jdhar@iiitm.ac.in

Harbax Singh
Department of Applied Mathematics,
Baba Banda Singh Bahadur Engineering College,
Fatehgarh Sahib-140407, Punjab, India
E-mail: bhattihs100@yahoo.com

Abstract
In this paper, a mathematical model is proposed to study the existence and stability of a non-uniform steady state of two competing species system in a two patch habitat, with diffusion and a non-diffusing self-renewable logistically growing common resource for each of the competing population in both the patches. Further, assumed that both the competing populations follow a general type of logistic growth in each of the habitat. It has been shown that there exists a positive, monotonic, continuous steady state solution with continuous flux matching at the interface for both the species separately and we also obtain the criteria for asymptotic stability in both liner and nonlinear cases. Moreover, it is also shown that in presence of supplementary resource, the level of steady state distribution increases and the effect of patchiness is destabilizing even in presence of a common self-renewable supplementary resource for both the species.

AMS Subject Classification: 92, 92A.
Keywords: Competition model, population diffusion, supplementary resource, asymptotic stability.