Water level in rivers, lakes and reservoirs has great influence on the interactions between prey and predator fish. Indeed, the increase of the water volume hinders the capture of the prey by the predator. The same reasoning applies when there is a decrease in the volume of water, favoring the capture of the prey by the predator. In this paper, we consider a seasonally varying predator–prey model to study the influence of water-level variations on the interaction between two species of fishes in an artificial lake. A seasonal variation of the water-level is introduced in the predation rate taking into account two values, leading to a general switched system. Permanence, stability and existence of an invariant domain containing at least one periodic solution are established. Our theoretical results confirm the assumption that the water exerts a strong influence on the interaction between fishes.

中文翻译：

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具有季节性水位波动的捕食者 - 猎物动态

河流、湖泊和水库的水位对猎物和捕食鱼类之间的相互作用有很大的影响。事实上，水量的增加阻碍了捕食者捕获猎物。当水量减少时，同样的推理也适用，有利于捕食者捕获猎物。在本文中，我们考虑一个季节性变化的捕食者 - 猎物模型来研究水位变化对人工湖中两种鱼类之间相互作用的影响。考虑到两个值，在捕食率中引入了水位的季节性变化，从而形成了一个通用的切换系统。建立了包含至少一个周期解的不变域的持久性、稳定性和存在性。