AI 中文总结
本文建立并分析了具有幼虫同类相食行为的鱼类种群数学模型，证明了平衡点全局稳定性，发现食物质量影响种群同类相食行为与生存，模型适用于热带骨雀鳝幼虫，可推广至其他同类相食鱼类。
AI 中文摘要
本文分析了一个具有幼虫阶段同类相食行为的鱼类种群数学模型，该种群被划分为三类：易受捕食者、同类相食者和非易受捕食者。假设初始时整个种群均为易受捕食者，随着发育，个体将转变为其他类别的一员。此外，非易受捕食者与同类相食者之间的相互作用为具有Beddington-DeAngelis功能反应的捕食-猎物关系。本文证明了平衡点的全局稳定性，数值模拟显示食物质量如何影响种群的同类相食行为及其生存情况。此外，结果表明该模型的解与热带骨雀鳝（Atractosteus tropicus）幼虫阶段的实验数据相吻合，该模型可适用于其他具有同类相食行为的鱼类物种。
英文摘要
A mathematical model is analyzed for a population of fish exhibiting cannibalism during its larval stage. The population is divided into three classes (vulnerable, cannibals, and non-vulnerable). It is assumed that initially, the entire population is vulnerable, and as they develop, individuals transition into one of the other classes. In addition, the interaction between the non-vulnerable and the cannibals is a predator-prey relationship with a Beddington-DeAngelis functional response. The global stability of the equilibrium point is demonstrated and numerical simulations show how food quality influences the cannibalistic behaviour of the population and its survival. Furthermore, it is shown that the solutions fit the data obtained experimentally for \textit{Atractosteus tropicus} in its larval state. This model can be adapted for other fish species that exhibit cannibalism.
