Global dynamics of a two-species Lotka-Volterra competition-diffusion-advection system with general carrying capacities and intrinsic growth rates II: Different diffusion and advection rates

Abstract

We study a two-species competition-diffusion-advection system with general intrinsic growth rates and carrying capacities in heterogeneous closed environments, where the two aquatic species have different advection and/or diffusion rates. Some special cases have been widely investigated, for example: the non-advective case [8,9], the homogeneous case [23,24,40], the proportional case [20,25]. However, due to the difficulty caused by the diffusion-advection type operators as well as the heterogeneous environments, the approaches developed in the previous papers cannot be directly applied to the general case here. With some new techniques, we characterize the linear stability of the two semi-trivial steady states and establish the non-existence of co-existence steady states in several scenarios. Based on these preparations and the theory of monotone dynamical systems, we establish the main results. Our results indicate that both competitive exclusion and coexistence may occur. Specially, we show a new way for coexistence of two species.