A two species competition model with diffusion and a common supplementary resource in two-patch habitat

In this paper, a mathematical model is proposed to study the existence and stability of the 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 population follows 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 both linear and nonlinear cases. Further, shown that in presence of supplementary resource the level of steady state distribution increase and the effect of patchiness is destabilized even in presence of a common self-renewable supplementary resource for both the species.