In this paper, we study a class of 3-species multidelay Lotka–Volterra ratio-dependent predator-prey model with feedback controls and prey diffusion. By using the theory of delay differential inequalities and developing some new analysis methods as well as constructing a suitable Lyapunov function, some sufficient conditions are obtained to guarantee the permanence of the system and the global attractivity of the positive solution for the predator-prey system. Furthermore, the corresponding periodic system is discussed, and some conditions are established about the existence, uniqueness, and stability of the positive periodic solution for the periodic system by using the fixed-point theory and theoretical analysis. In additional, some numerical solutions of the equations describing the system are given to verify the obtained criteria. Finally, the corresponding stochastic time-delay predator-prey model with multiplicative noise sources is solved numerically, and some interesting new dynamics behavior is obtained.

中文翻译：

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具有反馈控制和食饵扩散的时滞三种群捕食者-食饵模型的分析。

在本文中，我们研究了一类具有反馈控制和食饵扩散的三种群多时滞Lotka–Volterra比率依赖捕食者—食饵模型。通过使用时滞微分不等式理论，开发一些新的分析方法，并构造一个合适的Lyapunov函数，为保证系统的持久性和捕食被捕食系统的正解的整体吸引性，获得了一些充分条件。进一步，讨论了相应的周期系统，并利用定点理论和理论分析，建立了周期系统正周期解的存在性，唯一性和稳定性。另外，给出了描述系统的方程的一些数值解，以验证所获得的标准。最后，