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We study a general Lotka-Volterra competition-diffusion-advection system with general boundary conditions from river ecology. A complete classification on all possible long-time dynamical behaviors is established. Moreover, we investigate the joint effects of diffusion rates, advection rates, the inter-specific competition intensities and boundary conditions on global dynamics of the system. Finally, several numerical simulations are performed to verify the theoretical results. These results improve previously known ones by removing one condition and considering an interesting boundary condition where the species can be exposed to a net loss of individuals.
Wei et al. (2024) studied this question.