PREDATOR-PREY DYNAMICS WITH SEASONAL WATER-LEVEL FLUCTUATIONS

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.