格上三物种Lotka-Volterra竞争系统的行波
Traveling Waves for a Three Species Lotka-Volterra Competition System on the Lattice
DOI: 10.12677/aam.2025.1410417, PDF,   
作者: 廖 怡：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: Lotka-Volterra竞争系统；Schauder不动点定理；压缩矩形法；行波解；Lotka-Volterra Competition System； Schauder’s Fixed Point Theorem； Contracting Rectangles； Traveling Waves
摘要: 本文考虑三物种之间均存在竞争关系的格上Lotka-Volterra竞争系统行波的存在性，主要研究两个外来物种入侵一个弱本土物种和一个外来物种入侵两个弱本土物种这两种情况。首先，在构造上下解的帮助下，利用Schauder不动点定理证明了行波解的存在性；其次，采用压缩矩形法验证了在负无穷远处的稳定波尾极限；最后，通过反证法证明了在某些条件下行波的不存在性。
Abstract: The work is concerned with the existence of two types of traveling waves for Lotka-Volterra competitive system on the lattice with competition among three species. We examine the cases of two alien species invading one weak native species and one alien species invading two weak native species. Firstly, the existence of traveling waves is proved by Schauder’s fixed point theorem with the help of constructing upper-lower solutions. Secondly, using the method of the contracting rectangles, we derive the stable wave tail limit at negative infinity. Finally, the nonexistence of travelling waves is proved under certain conditions.
文章引用：廖怡. 格上三物种Lotka-Volterra竞争系统的行波[J]. 应用数学进展, 2025, 14(10): 31-47. https://doi.org/10.12677/aam.2025.1410417

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