Dynamical behaviors of a classical Lotka–Volterra competition–diffusion–advection system |
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Institution: | 1. School of Mathematics and Information Science, Shaanxi Normal University, Xi''an Shaanxi 710119, PR China;2. School of Arts and Sciences, Shaanxi University of Science and Technology, Xi''an Shaanxi 710021, PR China |
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Abstract: | This paper deals with a two-species competition model in a homogeneous advective environment, where two species are subjected to a net loss of individuals at the downstream end. Under the assumption that the advection and diffusion rates of two species are proportional, we give a basic classification on the global dynamics by employing the theory of monotone dynamical system. It turns out that bistability does not happen, but coexistence and competitive exclusion may occur. Furthermore, we present a complete classification on the global dynamics in terms of the growth rates of two species. However, once the above assumption does not hold, bistability may occur. In detail, there exists a tradeoff between growth rates of two species such that competition outcomes can shift between three possible scenarios, including competitive exclusion, bistability and coexistence. These results show that growth competence is important to determine dynamical behaviors. |
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Keywords: | Competition–diffusion–advection system Global asymptotic stability The theory of monotone dynamical system Growth competence Coexistence |
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