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Significant variations of the water-level of the lake can have a strong impact on the persistence of species. Indeed, when the water-level is low, during the autumn, the contact between the predator and the prey is more frequent, and the predation increases. Conversely, when the water-level is high, in the spring, it is more difficult for the predator to find a prey and the predation decreases. 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. The predator population is provided some additional food apart from the focal prey, and follows logistic growth in the absence of prey population. As control upon the over predation, the predator population is harvested. Sensitivity analysis shows that the biomass of predator population is highly sensitive to the additional food and water variations. In the absence of additional food, our results show bursting patterns of fishes whereas positive periodic solution arises if the additional food is available in sufficient amount. The positive periodic solution is shown to be globally stable. Higher values of water-level fluctuations induce double periodic oscillations. Our findings show that providing additional food source to the generalist predator together with water-level fluctuations exerts a strong influence on the interaction between fishes.

Water level regulates the dynamics of different populations residing in water bodies. The increase/decrease in the level of water leads to an increase/decrease in the volume of water, which influences the interactions of fishes and catching capability. We examine how seasonal variations in water level and harvesting affect the outcome of prey–predator interactions in an artificial lake. A seasonal variation of the water level is introduced in the predation rate. We derive conditions for the persistence and extinction of the populations. Using the continuation theorem, we determine the conditions for which the system has a positive periodic solution. The existence of a unique globally stable periodic solution is also presented. Moreover, we obtain conditions for the existence, uniqueness and stability of a positive almost periodic solution. We find that if the autonomous system has a stable focus, the corresponding nonautonomous system exhibits a unique stable positive periodic solution. But, whenever the autonomous system shows limit cycle oscillations, the corresponding nonautonomous system exhibits chaotic dynamics. The chaotic behavior of system is confirmed by the positivity of the maximal Lyapunov exponent. For higher values of the assimilation fraction of prey population, the persistent oscillations of the autonomous system are eliminated and this system becomes stable. On the other hand, chaotic nature of the nonautonomous system is converted into periodicity if the assimilation fraction of prey is large. Moreover, populations behave almost periodically if the seasonally varied rate parameters are almost periodic functions of time. Our findings show that water level plays an important role in the persistence of prey–predator system.

In this paper, the impact of environmental noise on prey–predator interactions with seasonal fluctuations in water levels has been studied. Both intensity of noise and water level variations together play a significant role in the dynamics of an aquatic prey–predator system. Analytically, we have shown the existence of a positive solution and its uniqueness, the ultimate bound of the system’s solutions, and the global attractivity of the solution. Moreover, parametric conditions for which model species either persist (strongly or weakly) in the system or go into extinction are derived and their biological significance is also discussed. The sufficient condition of stochastic permanence is also analyzed. To justify the analytical results, we have performed numerical simulations of both deterministic and stochastic systems and observed some significant dynamics in the considered system.

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