Permanence of Diffusive Models for Three Competing Species in Heterogeneous Environments

We address the question of the long‐term coexistence of three competing species whose dynamics are governed by the partial differential equations. We obtain criteria for permanent coexistence in a Lotka‐Volterra system modeling the interaction of three competing species in a bounded habitat whose exterior is lethal to each species. It is also proved that if the intercompeting strength is very weak, the system is always permanent, provided that each single one of the three species can survive in the absence of the two other species.