具有毒性趋化性的空间捕食模型中的光驱动相互作用
Light driven interactions in spatial predator-prey model with toxicant chemotaxis
摘要：
我们开发和分析的光驱动的生态毒理学过程的时空模型，受到污染物的藻类和\textsl{Daphnia}的水生捕食-被捕食系统的动机。种群动力学是由光驱动的，光在时间上是周期性的，并随空间深度而变化。在参数约束下，证明了空间和时间依赖周期解的存在唯一性，并给出了解的解析函数。我们进行图灵稳定性分析的解决方案的初始条件的扰动。给定一个周期性的平衡状态的扰动，我们表明，系统将返回到这个平衡状态，只要运动是足够快和/或水库深度足够浅。分析结果假设一些Dirichlet边界条件，匹配的周期性平衡状态，然而，更宽松的边界条件的数值模拟捕获类似的周期性解决方案。这项工作揭示了空间依赖的种群动力学，是由周期性的力量，如光水平。
英文摘要：
We develop and analyze a spatial temporal model of light driven ecotoxicological processes, motivated by an aquatic predator-prey system of algae and \textsl{Daphnia} subject to a contaminant. Population dynamics are driven by light, which is periodic in time and varies with spatial depth. The existence and uniqueness of spatial and temporal dependent periodic solutions are shown and analytical functions of the solutions under parameter constraints are presented. We conduct Turing stability analyses of solutions with respect to perturbations of initial conditions. Given a perturbation to a periodic equilibrium state, we show the system will return to this equilibrium state as long as motility is fast enough and/or the reservoir depth is shallow enough. Analytical results assume some Dirichlet boundary conditions that match the periodic equilibrium state, however numerical simulations with more relaxed boundary conditions capture similar periodic solutions. The work sheds light onto spatially dependent population dynamics that are driven by periodic forces, such as light levels.
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