Effects of consecutive water level fluctuations and harvesting on predator-prey interactions

In lakes, water level can alter the physical environment and may influence predatory fish performance. In this paper, we ask how do variations in water level affect population cycles? We use a predator-prey model that includes fishing terms as a case study. With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, we establish sufficient conditions for the existence of at least four positive periodic solutions. Our theoretical results confirm the assumption that the water level exerts a strong influence on the interaction between fishes. An example is given to illustrate the effectiveness of our results.