Stability of traveling wave solutions for a nonlocal Lotka-Volterra model

被引：0

作者：

Ma, Xixia ^{[1
]}

Liu, Rongsong ^{[2
]}

Cai, Liming ^{[1
]}

机构：

[1] Xinyang Normal Univ, Sch Math & Stat, Xinyang 464000, Peoples R China

[2] Univ Wyoming, Dept Math & Stat, Laramie, WY 82070 USA

来源：

MATHEMATICAL BIOSCIENCES AND ENGINEERING | 2024年 / 21卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Traveling waves; nonlocal; stability; energy estimates; global boundedness; SPREADING SPEED; EQUATION; FRONTS; EXISTENCE; SYSTEM;

D O I：

10.3934/mbe.2024020

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this paper, we studied the stability of traveling wave solutions of a two-species LotkaVolterra competition model in the form of a coupled system of reaction diffusion equations with nonlocal intraspecific and interspecific competitions in space at times. First, the uniform upper bounds for the solutions of the model was proved. By using the anti-weighted method and the energy estimates, the asymptotic stability of traveling waves with large wave speeds of the system was established.

引用

页码：444 / 473

页数：30

共 20 条

[1] The non-local Fisher-KPP equation: travelling waves and steady states [J].

Berestycki, Henri ;

Nadin, Gregoire ;

Perthame, Benoit ;

Ryzhik, Lenya .

NONLINEARITY, 2009, 22 (12) :2813-2844

[2] Asymptotic behaviour of travelling waves for the delayed Fisher-KPP equation [J].

Ducrot, Arnaud ;

Nadin, Gregoire .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 256 (09) :3115-3140

[3] MONOTONE TRAVELING WAVES FOR DELAYED LOTKA-VOLTERRA COMPETITION SYSTEMS [J].

Fang, Jian ;

Wu, Jianhong .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2012, 32 (09) :3043-3058

[4] EXISTENCE AND STABILITY OF TRAVELING WAVE SOLUTIONS OF COMPETITION MODELS - A DEGREE THEORETIC APPROACH [J].

GARDNER, RA .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1982, 44 (03) :343-364

[5] Convergence and travelling fronts in functional differential equations with nonlocal terms: A competition model [J].

Gourley, SA ;

Ruan, SG .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2003, 35 (03) :806-822

[6] RECENT DEVELOPMENTS ON WAVE PROPAGATION IN 2-SPECIES COMPETITION SYSTEMS [J].

Guo, Jong-Shenq ;

Wu, Chang-Hong .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2012, 17 (08) :2713-2724

[7] The Minimal Speed of Traveling Fronts for the Lotka-Volterra Competition System [J].

Guo, Jong-Shenq ;

Liang, Xing .

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2011, 23 (02) :353-363

[8] On the nonlocal Fisher-KPP equation: steady states, spreading speed and global bounds [J].

Hamel, Francois ;

Ryzhik, Lenya .

NONLINEARITY, 2014, 27 (11) :2735-2753

[9] TRAVELING WAVES FOR NONLOCAL LOTKA-VOLTERRA COMPETITION SYSTEMS [J].

Han, Bang-Sheng ;

Wang, Zhi-Cheng ;

Du, Zengji .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2020, 25 (05) :1959-1983

[10]

Hosono Y., 1989, Numer. Appl. Math., P687

← 1 2 →