格上三物种捕食–食饵系统的行波解
Traveling Wave Solutions for a Predator-Prey System of Three Species on Lattice
DOI: 10.12677/aam.2025.1410416, PDF,   
作者: 肖明珠：长沙理工大学数学与统计学院，湖南 长沙；长沙理工大学工程数学建模与分析湖南省重点实验室，湖南 长沙
关键词: 行波解；离散扩散；Schauder不动点定理；压缩矩形；Traveling Wave Solution； Discrete Diffusive； Schauder’s Fixed Point Theorem； Shrinking Rectangle
摘要: 本文研究了具有两个捕食者和一个食饵的离散扩散的捕食者–食饵模型的行波解，其中两个捕食者的净增长率均为负。当外来捕食者的传播速度大于等于最小波速时，系统存在连接无捕食者状态和共存状态的行波解，即捕食者入侵成功。在Schauder不动点定理的帮助下构造了合适的上下解，证明了行波解的存在性。另外，利用压缩矩形的方法得到了行波解在无穷远处的渐近行为。通过对最小波速的估计，得到了当外来捕食者的传播速度小于最小波速时，系统不存在行波解。
Abstract: In this paper, we study the traveling wave solution of a discrete diffusive predator-prey model with two predators and one prey, in which the net growth rate of both predators is negative. When the propagation speed of the invasive predator is greater than or equal to the minimum wave speed there exists a traveling wave solution connecting the predator-free state and the coexistence state of the system, meaning the predator invasion is successful. With the help of Schauder’s fixed point theorem, suitable upper and lower solutions are constructed to prove the existence of traveling wave solutions. In addition, the asymptotic behavior of the traveling wave solution at infinity is obtained by using the method of shrinking rectangle. By estimating the minimum wave speed, it is obtained that there is no traveling wave solution for the system when the spread speed of the invasive predator is less than the minimal wave speed.
文章引用：肖明珠. 格上三物种捕食–食饵系统的行波解[J]. 应用数学进展, 2025, 14(10): 16-30. https://doi.org/10.12677/aam.2025.1410416

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