具有移动环境的 Lotka-Volterra 合作系统周期强迫波的存在性

具有移动环境的 Lotka-Volterra 合作系统周期强迫波的存在性

Existence of Periodic Forced Waves for a Lotka-Volterra Cooperative System with Shifting Habitat

摘要/Abstract

参考文献 21

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数学物理学报 ›› 2025, Vol. 45 ›› Issue (2): 479-492.

王国正(),史振霞^*()

兰州交通大学数理学院兰州 730070

收稿日期:2024-01-30 修回日期:2024-10-15 出版日期:2025-04-26 发布日期:2025-04-09
通讯作者: 史振霞 E-mail:1152619979@qq.com;shizhx08@mail.lzjtu.cn
作者简介:王国正，E-mail:1152619979@qq.com
基金资助:
国家自然科学基金(11904275)

Guozheng Wang(),Zhenxia Shi^*()

School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070

Received:2024-01-30 Revised:2024-10-15 Online:2025-04-26 Published:2025-04-09
Contact: Zhenxia Shi E-mail:1152619979@qq.com;shizhx08@mail.lzjtu.cn
Supported by:
NSFC(11904275)

摘要：

该文主要研究具有移动环境的 Lotka-Volterra 合作系统在二维格上的周期强迫波的存在性. 首先, 证明 Lotka-Volterra 系统的初值问题解的存在性与唯一性, 并建立了比较原理. 其次, 构造 Lotka-Volterra 合作系统的一对上下解, 通过单调迭代技巧并结合上、下解方法证明了与栖息地移动速度相一致的周期强迫波的存在性.

关键词: 存在性, 周期强迫波, Lotka-Volterra 合作系统, 单调迭代技巧, 上下解方法

Abstract:

This paper is concerned with the existence of periodic forced waves on a two-dimensional lattice for Lotka-Volterra cooperative systems with a shifting habitat. First, we prove the existence and uniqueness of solutions to the initial value problem for the Lotka-Volterra system and establish a comparison principle. Second, we construct a pair of upper and lower solutions of the Lotka-Volterra cooperative system and prove the existence of periodic forced waves consistent with the habitat movement velocity by monotone iteration technique and combining the upper and lower solution methods.

Key words: existence, periodic forced waves, Lotka-Volterra cooperative system, monotone iteration technique, upper and lower solutions

中图分类号:

0175

王国正,史振霞. 具有移动环境的 Lotka-Volterra 合作系统周期强迫波的存在性[J]. 数学物理学报, 2025, 45(2): 479-492.

Guozheng Wang,Zhenxia Shi. Existence of Periodic Forced Waves for a Lotka-Volterra Cooperative System with Shifting Habitat[J]. Acta mathematica scientia,Series A, 2025, 45(2): 479-492.

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