Abstract In this study, we investigate the global dynamics of non-autonomous and autonomous systems based on the Leslie–Gower type model using the Beddington–DeAngelis functional response (BDFR) with time-independent and time-dependent model parameters. Unpredictable disturbances are introduced in the forms of feedback control variables. BDFR explains the feeding rate of the predator as functions of both the predator and prey densities. The global stability of the unique positive equilibrium solution of the autonomous model is determined by defining an appropriate Lyapunov function. The condition obtained for the global stability of the interior equilibrium ensures that the global stability is free from control variables, which is also a significant issue in the ecological balance control procedure. The autonomous system exhibits complex dynamics via bifurcation scenarios, such as period doubling bifurcation. We prove the existence of a globally stable almost periodic solution of the associated non-autonomous model. The different coefficients of the system are taken as almost periodic functions by generalizing periodic assumptions. The permanence of the non-autonomous system is established by defining upper and lower averages of a function. Our results also explain how the important hypothesis in ecology known as the “intermediate disturbance hypothesis” applies in predator–prey interactions. We show that moderate feedback intensity can make both the ordinary differential equation system and partial differential equation system more robust. The results obtained provide new insights into the protection of populations, where moderate feedback intensity can promote the coexistence of species and adjusting the intensity of the feedback in appropriate regions can control the population biomass while maintaining the stability of the system. Finally, the results obtained from extensive numerical simulations support the analytical results as well as the usefulness of the present study in terms of ecological balance and bio-control problems in agro-ecosystems.

中文翻译：

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具有相互干扰捕食者的捕食者-猎物相互作用系统：反馈控制的作用

摘要 在这项研究中，我们使用具有时间无关和时间相关模型参数的贝丁顿-德安吉利斯函数响应 (BDFR) 研究基于 Leslie-Gower 类型模型的非自治和自治系统的全局动力学。不可预测的干扰以反馈控制变量的形式引入。BDFR 将捕食者的摄食率解释为捕食者和猎物密度的函数。自治模型唯一正均衡解的全局稳定性是通过定义一个合适的李雅普诺夫函数来确定的。内部平衡的全局稳定性得到的条件保证了全局稳定性不受控制变量的影响，这也是生态平衡控制过程中的一个重要问题。自治系统通过分叉场景表现出复杂的动态，例如周期加倍分叉。我们证明了相关非自治模型的全局稳定的几乎周期解的存在。通过概括周期性假设，系统的不同系数被视为几乎是周期性的函数。非自治系统的持久性是通过定义函数的上限和下限来建立的。我们的结果还解释了生态学中被称为“中间干扰假设”的重要假设如何应用于捕食者-猎物相互作用。我们表明适度的反馈强度可以使常微分方程系统和偏微分方程系统更加鲁棒。获得的结果为保护人口提供了新的见解，其中适度的反馈强度可以促进物种共存，在适当的区域调整反馈强度可以控制种群生物量，同时保持系统的稳定性。最后，从广泛的数值模拟中获得的结果支持分析结果以及本研究在农业生态系统中的生态平衡和生物控制问题方面的有用性。