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.

中文翻译：

---

水位波动影响的猎物和捕食者相互作用的非自治模型中的混沌

水位调节居住在水体中的不同种群的动态。水位的增加/减少会导致水量的增加/减少，这会影响鱼类和捕捞能力的相互作用。我们研究了水位和捕捞的季节性变化如何影响人工湖中猎物 - 捕食者相互作用的结果。在捕食率中引入了水位的季节性变化。我们推导出种群持续存在和灭绝的条件。使用连续定理，我们确定系统具有正周期解的条件。还提出了唯一的全局稳定周期解的存在。此外，我们获得了一个正的几乎周期解的存在性、唯一性和稳定性的条件。我们发现，如果自治系统具有稳定的焦点，则相应的非自治系统表现出唯一的稳定正周期解。但是，每当自治系统表现出极限环振荡时，相应的非自治系统就会表现出混沌动力学。最大李雅普诺夫指数的正性证实了系统的混沌行为。对于较高的猎物种群同化分数值，自治系统的持续振荡被消除，该系统变得稳定。另一方面，如果猎物的同化比例很大，则非自治系统的混沌性质会转化为周期性。此外，如果季节性变化的速率参数几乎是时间的周期性函数，那么种群的行为几乎是周期性的。