A discrete delay is included to model the time between the capture of the prey and its conversion to viable biomass in the simplest classical Gause type predator-prey model that has equilibrium dynamics without delay. As the delay increases from zero, the coexistence equilibrium undergoes a supercritical Hopf bifurcation, two saddle-node bifurcations of limit cycles, and a cascade of period doublings, eventually leading to chaos. The resulting periodic orbits and the strange attractor resemble their counterparts for the Mackey-Glass equation. Due to the global stability of the system without delay, this complicated dynamics can be solely attributed to the introduction of the delay. Since many models include predator-prey like interactions as submodels, this study emphasizes the importance of understanding the implications of overlooking delay in such models on the reliability of the model-based predictions, especially since temperature is known to have an effect on the length of certain delays.

中文翻译：

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具有离散时滞的简单捕食-被捕食模型的混沌动力学

在最简单的经典Gause型捕食者－猎物模型中，包括一个离散的延迟来模拟捕获猎物与将其转化为可行的生物量之间的时间，该模型具有无延迟的平衡动力学。当延迟从零开始增加时，共存均衡经历超临界Hopf分叉，两个极限周期的鞍节点分叉以及一连串的周期加倍，最终导致混乱。产生的周期轨道和奇异的吸引子类似于它们的Mackey-Glass方程的对应轨道。由于系统没有延迟的全局稳定性，这种复杂的动态可以完全归因于延迟的引入。由于许多模型都将类似交互的捕食者-猎物作为子模型，