We investigate a reaction-diffusion-advection system describing the interaction between a population and a toxicant in open advective environments. The interesting feature of this model is the consideration of a more general advective term and boundary condition. By applying the theory of monotone semi-flow and principal eigenvalue, we obtain the existence and stability of steady states and further present a clear picture on the local and global dynamics. We explore the effects of toxicants on populations and give some sufficient conditions for the existence or extinction of the population.

中文翻译：

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开放平流环境中时空模型的动力学行为

我们研究了一个反应扩散平流系统，描述了开放平流环境中种群与有毒物质之间的相互作用。该模型的有趣特征是考虑了更一般的平流项和边界条件。通过应用单调半流和主特征值理论，我们获得了稳态的存在性和稳定性，并进一步清晰地描绘了局部和全局动力学。我们探讨有毒物质对种群的影响，并为种群的存在或灭绝提供一些充分条件。