具有食饵年龄结构和趋化项的捕食者–食饵模型的全局有界性

Global Boundedness of a Predator-Prey Model with Stage Structure and Taxis Term for the Prey

捕食者–食饵的相互作用是一个复杂生态系统的基本组成模块之一。考虑到捕食者和食饵种群的年龄结构对它们之间相互作用的影响,文章建立了一个具有食饵年龄结构和趋化项的捕食者–食饵模型。该模型将食饵成长分为两个阶段:未成熟和成熟,且一部分未成熟食饵会成长为成熟食饵。在Neumann边界条件下的光滑有界区域上,用构造辅助函数的方法证明了该模型解的全局存在性和有界性。该结果适用于任意空间维度的系统。Predator-prey interactions are one of the fundamental building blocks of a complex ecosystem. In this paper, considering the influence of the stage structure of predator and prey populations on their interactions, a predator-prey model with prey stage structure and taxis term was developed. The model divides prey growth into two stages: immature and mature, and a portion of immature prey grows into mature prey. The global existence and boundedness of the solution are proved by constructing an auxiliary function on a smooth bounded region under no-flux boundary conditions. The result holds for the system in any spatial dimension.