一种针对美洲狮（Puma Concolor）的时滞捕食者-猎物模型的稳定性
Stability of a Delayed Predator-Prey Model for Puma Concolor
AI总结：
本研究构建了带时滞的美洲狮-猎物数学模型，推导了正平衡点绝对稳定性条件与唯一最大解的存在性，并通过数值模拟验证定理，探究移除部分捕食者或猎物的影响。
摘要：
本研究提出了一个描述美洲狮（Puma concolor）与其猎物之间关系的数学模型，该模型采用时滞微分方程、Holling III型功能反应、猎物的逻辑斯蒂增长，以及Ricker型函数来模拟美洲狮的种内竞争。针对正平衡点，本研究基于时滞值和模型参数，建立了保证其绝对稳定性的条件。分析表明，所提出的模型存在唯一的最大解，该解在非负初始条件下保持非负，且对所有大于0的$t$都有明确定义。此外，本研究采用不同参数值进行了数值模拟，以探究系统性移除一定比例的捕食者或猎物所产生的影响。数值模拟旨在例证并应用本文所证明的定理。
英文摘要：
This study presents a mathematical model that describes the relationship between the Puma concolor and its prey using delay differential equations, a Holling type III functional response, logistic growth for the prey, and a Ricker-type function to model intraspecific competition of the pumas. For positive equilibrium, conditions guaranteeing absolute stability are established, based on the delay value and model parameters. The analysis demonstrates the existence of a unique maximal solution for the proposed model, which remains non-negative for nonnegative initial conditions and is well-defined for all $t$ greater than zero. Furthermore, numerical simulations with different parameter values were performed to investigate the effects of systematically removing a percentage of predators or prey. Numerical simulations attempt to exemplify and put into practice the theorems proved in this article.
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