Global Stability of Traveling Waves for the Lotka–Volterra Competition System with Three Species-Reference-Cited by-同舟云学术

Global Stability of Traveling Waves for the Lotka–Volterra Competition System with Three Species

Published:2023-05-06 Issue:9 Volume:11 Page:2189
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Hu Shulin¹,Pan Chaohong¹^ORCID,Wang Lin²

Affiliation:

1. School of Mathematics and Physics, University of South China, Hengyang 421001, China

2. Basic Department, Hunan Institute of Traffic Engineering, Hengyang 421001, China

Abstract

The stability of traveling waves for the Lotka–Volterra competition system with three species is investigated in this paper. Specifically, we first show the asymptotic behavior of traveling wave solutions and then establish the local stability and the global stability under the weighted functional space. For local stability, the spectrum approach is used, while for global stability, the comparison principle and squeezing theorem are combined.

Funder

Teaching Research and Reform Project of South China University of Technology

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/9/2189/pdf

Reference42 articles.

1. Minimal-speed selection oftraveling waves to the Lotka-Volterra competition model;Alhasanat;J. Differ. Equ.,2019

2. Stability of Traveling Waves to the Lotka-Volterra Competition Model;Alhasanat;Complexcity,2019

3. On the conjecture for the pushed wavefront to the diffusive Lotka-Volterra competition model;Alhasanat;J. Math. Biol.,2020

4. Existence and stability of time periodic traveling waves for a periodic bistable Lotka-Volterra competition system;Bao;J. Differ. Equ.,2013

5. Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation;Li;Discret. Contin. Dyn. Syst. Ser. A,2009