We consider a model of two competing species of Lotka--Volterra type with diffusion (migration), where the spatial domain is an arbitrary finite graph (network). Depending on the parameters of the model, we describe the spatially homogeneous stationary states and their stability, discuss the existence and number of spatially heterogeneous stationary states, and study the asymptotic behavior of solutions.
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Antonín Slavík (2020) studied this question.
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