Traveling Wave Solutions for Mixed Diffusive Competition Systems with Spatio-temporal Delays

SHI Lingling, WANG Yang, YAO Meiping

PDF(694 KB)
PDF(694 KB)
Journal of Shanxi University(Natural Science Edition) ›› 2025, Vol. 48 ›› Issue (3) : 429-434. DOI: 10.13451/j.sxu.ns.2024010
Mathematics and Applied Mathematics

Traveling Wave Solutions for Mixed Diffusive Competition Systems with Spatio-temporal Delays

Author information +
History +

Abstract

In this paper, the existence of traveling wave solutions of mixed diffusive competition systems with spatio-temporal delays was studied. Firstly, in order to eliminate the influence of spatio-temporal delays, the delayed diffusion system with two equations was changed into the non-delay diffusion system with four equations based on the property of the kernels in spatio-temporal delays. Then the system was further changed into the monotone system. Finally, the main results were obtained by using the super- and sub-solutions method and the fixed point theorem.

Key words

reaction diffusion system / super- and sub-solutions / nonlocal delays

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations
SHI Lingling , WANG Yang , YAO Meiping. Traveling Wave Solutions for Mixed Diffusive Competition Systems with Spatio-temporal Delays. Journal of Shanxi University(Natural Science Edition). 2025, 48(3): 429-434 https://doi.org/10.13451/j.sxu.ns.2024010

References

List( Publishing order | Descend order by publishing year | Descend order by cited within ) Chart analysis
1
BRITTON N F. Aggregation and the Competitive Exclusion Principle[J]. J Theor Biol, 1989, 136(1): 57-66. DOI: 10.1016/s0022-5193(89)80189-4 .
本文引用 [1]
2
BRITTON N F. Spatial Structures and Periodic Travelling Waves in an Integro-differential Reaction-diffusion Population Model[J]. SIAM J Appl Math, 1990, 50(6): 1663-1688. DOI: 10.1137/0150099 .
本文引用 [1]
3
ROQUES L, HOSONO Y, BONNEFON O, et al. The Effect of Competition on the Neutral Intraspecific Diversity of Invasive Species[J]. J Math Biol, 2015, 71(2): 465-489. DOI: 10.1007/s00285-014-0825-4 .
本文引用 [1]
4
ALHASANAT A, OU C H. Minimal-speed Selection of Traveling Waves to the Lotka-Volterra Competition Model[J]. J Differ Equ, 2019, 266(11): 7357-7378. DOI: 10.1016/j.jde.2018.12.003 .
本文引用 [1]
5
LI K, HE Y L. Traveling Waves in Nonlocal Delayed Reaction-Diffusion Bistable Equations and Applications[J]. Math Methods App Sciences, 2024, 47(4): 2769-2786. DOI: 10.1002/mma.9777 .
本文引用 [3]
6
HOU X J, LI Y. Traveling Waves in a Three Species Competition-cooperation System[J]. Commun Pure Appl Anal, 2017, 16(4): 1103-1120. DOI: 10.3934/cpaa.2017053 .
本文引用 [1]
7
CHANG C H, HSU C H, YANG T S. Traveling Wavefronts for a Lotka-Volterra Competition Model with Partially Nonlocal Interactions[J]. Z Für Angew Math Und Phys, 2020, 71(2): 70. DOI: 10.1007/s00033-020-1289-6 .
本文引用 [5]
8
HAO Y C, ZHANG G B. The Dynamics of Traveling Wavefronts for a Nonlocal Delay Competition System with Local vs. Nonlocal Diffusions[J]. Commun Nonlinear Sci Numer Simul, 2022, 110: 106381. DOI: 10.1016/j.cnsns.2022.106381 .
本文引用 [3]
9
骆兰兰. 非局部Lotka-Volterra竞争系统的波前解[D]. 兰州: 兰州大学, 2022.
LUO L L. Wavefront Solution of Nonlocal Lotka-Volterra Competitive System[D].Lanzhou: Lanzhou University, 2022.
本文引用 [2]
10
MA S W. Traveling Wavefronts for Delayed Reaction-diffusion Systems via a Fixed Point Theorem[J]. J Differ Equ, 2001, 171(2): 294-314. DOI: 10.1006/jdeq.2000.3846 .
本文引用 [2]
11
HUANG J H, ZOU X F. Existence of Traveling Wavefronts of Delayed Reaction Diffusion Systems without Monotonicity[J]. Discrete Contin Dyn Syst A, 2003, 9(4): 925-936. DOI: 10.3934/dcds.2003.9.925 .
12
AI S B. Traveling Wave Fronts for Generalized Fisher Equations with Spatio-temporal Delays[J]. J Differ Equ, 2007, 232(1): 104-133. DOI: 10.1016/j.jde.2006.08.015 .
本文引用 [1]

Comments

PDF(694 KB)

Accesses

Citation

Detail
Sections
Recommended
Copyright © Journal of Shanxi University(Natural Science Edition), All Rights Reserved.
Powered by Beijing Magtech Co. Ltd.

/

〈 〉