Dispersal plays an essential role in population dynamics. The dispersal effect is particularity important when 
the distribution of resources is not uniform in space. Hastings \cite{Hastings} and Dockery, et al. \cite{Dockery}, 
used a simple one dimensional model of two species, identical except for dispersal rate, compete for a spatially 
distributed resource. They proved, solving the reaction-diffusion equations, that the more slowly species drives 
the other species to extinction for any non-uniform distribution of resources that is smooth enough. Kessler and 
sander \cite{kessler&sander}, demonstrated that by formulate the original model differently, in terms of an 
agent-based simulation, over a wide range of parameters got the opposite behavior. That is, the fast species drive 
the slow species to extinction. Expansion of the model to two dimensional lead to a new phenomenon that wasn't 
occur in the one dimensional model: coexistence in part of the parameters.