论文标题
与离散延迟的简单捕食者模型中的混沌动力学
Chaotic dynamics in a simple predator-prey model with discrete delay
论文作者
论文摘要
包括一个离散延迟，以模拟捕获猎物的捕获与最简单的经典Gause类型捕食者捕食者模型中的捕获时间之间的时间，该模型具有平衡动力学，毫不延迟。随着延迟的增加，共存平衡会经历超临界的霍夫夫分叉，两个极限循环的鞍形节点分叉以及一系列的时期双重速率，导致混乱。由此产生的周期性轨道和奇怪的吸引子类似于Mackey-Glass方程的对应物。由于系统的全局稳定性毫不延迟，这些复杂的动态仅归因于延迟的引入。由于许多模型都包含捕食者 - 捕食者像子模型一样的相互作用，因此本研究强调了理解此类模型对基于模型预测的可靠性的影响的重要性，尤其是因为已知温度对某些延迟的长度有影响。
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, eventu1ally 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, these 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 the temperature is known to have an effect on the length of certain delays.
