华东师范大学学报（自然科学版） >

2020 , Vol. 2020 >Issue 4: 18 - 25

DOI: https://doi.org/10.3969/j.issn.1000-5641.201911019

数学

一类具有强时滞核的单种群扩散模型的行波解

  • 杨高翔
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  • 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
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

收稿日期: 2019-04-29

  网络出版日期: 2020-07-20

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)

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

  • YANG Gaoxiang
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  • 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 date: 2019-04-29

  Online published: 2020-07-20

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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

本文引用格式

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 . DOI: 10.3969/j.issn.1000-5641.201911019

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

参考文献

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