一类具有强时滞核的单种群扩散模型的行波解

doi:10.3969/j.issn.1000-5641.201911019

华东师范大学学报（自然科学版） ›› 2020, Vol. 2020 ›› Issue (4): 18-25.doi: 10.3969/j.issn.1000-5641.201911019

一类具有强时滞核的单种群扩散模型的行波解

杨高翔^1,2

1. 安康学院数学与统计学院,陕西安康 725000;
2. 安康学院数学与应用数学研究所,陕西安康 725000

收稿日期:2019-04-29 发布日期:2020-07-20
作者简介:杨高翔，男，博士，副教授，研究方向为非线性动力学与生物数学. E-mail: stx_ygx@aku.edu.cn
基金资助:
陕西省自然科学基础研究计划(2019JM-444); 安康学院科研项目(2018AYPY01, 2017AYQN09, 2018AYQN02)

Travelling wave solutions of a diffusive single species model with a strong generic delay kernel

YANG Gaoxiang^1,2

1. School of Mathematics and Statistics, Ankang University, Ankang, Shaanxi 725000, China;
2. Institute of Mathematics and Applied Mathematics, Ankang University, Ankang, Shaanxi 725000, China

Received:2019-04-29 Published:2020-07-20

摘要/Abstract

摘要： 本文中，建立了一类具有强时滞核的单种群扩散模型行波解的存在性. 首先, 在该模型没有时滞的情况下, 利用常微分方程的定性理论, 得到了该模型行波解的存在性. 然后, 在该模型中时滞非常小时, 结合线性链式法则和几何奇异摄动理论, 证明了该模型的行波解仍然存在.

关键词: 行波解, 强时滞核, 几何奇异摄动法

Abstract: In this paper, the existence of travelling wave solutions of a diffusive single species model with a strong generic delay kernel is established in two steps. Firstly, in the case of a species model without time delay, the existence of travelling wave solutions of the species model is obtained by using qualitative theories of ordinary differential equations. Secondly, when the time delay is greater than zero and sufficiently small, the existence of travelling wave solutions of the species model is verified by using linear chain techniques and the geometric singular perturbation theory.

Key words: travelling wave solutions, strong generic delay kernel, geometric singular perturbation theory

中图分类号:

O175.26

杨高翔. 一类具有强时滞核的单种群扩散模型的行波解[J]. 华东师范大学学报（自然科学版）, 2020, 2020(4): 18-25.

YANG Gaoxiang. Travelling wave solutions of a diffusive single species model with a strong generic delay kernel[J]. Journal of East China Normal University(Natural Science), 2020, 2020(4): 18-25.

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一类具有强时滞核的单种群扩散模型的行波解

Travelling wave solutions of a diffusive single species model with a strong generic delay kernel

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