Abstract
A general reaction–diffusion–advection system modeling the competition between two aquatic species in a river/stream is studied. Under certain mild conditions, we first establish a complete classification on all possible global dynamical behaviors of this system. Then by regarding the competition coefficients as bifurcation parameters, we present further a clear picture on the global dynamics. Our main results improve a previous work of Xu et al. (2020)by considering a much more general setting and more importantly removing the technical condition (see (A1) below).
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