In this study, we consider a directed–diffusion system describing the interactions between two organisms in heterogeneous environment. We first establish a linearly stability of the co-existence (positive) steady state. Then we further present a classification on all possible long-time dynamical behaviors by appealing to the theory of monotone dynamical systems.

中文翻译：

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Lotka–Volterra竞争扩散系统的全局定向动力学

在这项研究中，我们考虑一个定向扩散系统，该系统描述了异质环境中两种生物之间的相互作用。我们首先建立并存（正）稳态的线性稳定性。然后，我们通过单调动力系统理论进一步提出所有可能的长时间动力行为的分类。