Effects of migration of three competing species on their distributions in multizone environment

In this paper, we investigate the relationship between migration and species distribution in multizone environment. We present a discrete model for migration of three competing species over three zones. We prove that the migration tactics of species leads to the fact that the system exponentially converges to one of two typical configurations: the first one is a case where each zone contains only one species, the second one is a case where one species is of density 1 in one zone, another species stays and dominates in the two other zones, and the last species is evenly split into the 3 zones with a density one third in each. We also show a characterization of the initial conditions under which the system converges to one of the two configurations.