Uniqueness and Complete Dynamics in Heterogeneous Competition-Diffusion Systems

In this paper we study the interactions between diffusion and heterogeneity of the environment in the classical diffusive Lotka–Volterra competition systems. In the weak competition case, we establish the uniqueness, hence the global asymptotic stability, of coexistence steady states under various circumstances, and thereby we obtain a complete understanding of the change in dynamics when one of the interspecific competition coefficients is small.