Traveling wave in a ratio-dependent Holling–Tanner system with nonlocal diffusion and strong Allee effect

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED Nonlinear Analysis-Real World Applications Pub Date : 2025-02-06 DOI:10.1016/j.nonrwa.2025.104327

Hongliang Li , Min Zhao , Rong Yuan

{"title":"Traveling wave in a ratio-dependent Holling–Tanner system with nonlocal diffusion and strong Allee effect","authors":"Hongliang Li , Min Zhao , Rong Yuan","doi":"10.1016/j.nonrwa.2025.104327","DOIUrl":null,"url":null,"abstract":"<div><div>This paper explores a ratio-dependent Holling–Tanner predator–prey system with nonlocal diffusion, wherein the prey is subject to strong Allee effect. To be specific, by using Schauder’s fixed point theorem and iterative technique, we establish a theoretical framework regarding the existence of traveling waves. We meticulously construct upper and lower solutions and a novel sequence, and employ the squeeze method to validate the existence of traveling waves for <span><math><mrow><mi>c</mi><mo>></mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>. Additionally, by spreading speed theory and the comparison principle, we confirm the existence of traveling wave with <span><math><mrow><mi>c</mi><mo>=</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>. Finally, we investigate the nonexistence of traveling waves for <span><math><mrow><mi>c</mi><mo><</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>, and conclusively determine the minimal wave speed.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"84 ","pages":"Article 104327"},"PeriodicalIF":1.8000,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Real World Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1468121825000136","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

This paper explores a ratio-dependent Holling–Tanner predator–prey system with nonlocal diffusion, wherein the prey is subject to strong Allee effect. To be specific, by using Schauder’s fixed point theorem and iterative technique, we establish a theoretical framework regarding the existence of traveling waves. We meticulously construct upper and lower solutions and a novel sequence, and employ the squeeze method to validate the existence of traveling waves for

c > c^{*}

. Additionally, by spreading speed theory and the comparison principle, we confirm the existence of traveling wave with

c = c^{*}

. Finally, we investigate the nonexistence of traveling waves for

c < c^{*}

, and conclusively determine the minimal wave speed.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

求助全文

约1分钟内获得全文去求助

来源期刊

Nonlinear Analysis-Real World Applications 数学-应用数学

CiteScore

3.80

自引率

5.00%

发文量

176

审稿时长

59 days

期刊介绍： Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems. The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.