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

Xixia Ma; Rongsong Liu; Liming Cai; Xixia Ma; Rongsong Liu; Liming Cai

doi:10.3934/mbe.2024020

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 1: 444-473. doi: 10.3934/mbe.2024020

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Research article

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

1.
School of Mathematics and Statistics, Xinyang Normal University, Xinyang, China, 464000
2.
Department of Mathematics and Statistics, University of Wyoming, Laramie, WY, USA, 82070

Received: 06 October 2023 Revised: 10 November 2023 Accepted: 22 November 2023 Published: 14 December 2023

In this paper, we studied the stability of traveling wave solutions of a two-species Lotka-Volterra 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.
- Traveling waves,
- nonlocal,
- stability,
- energy estimates,
- global boundedness
Citation: Xixia Ma, Rongsong Liu, Liming Cai. Stability of traveling wave solutions for a nonlocal Lotka-Volterra model[J]. Mathematical Biosciences and Engineering, 2024, 21(1): 444-473. doi: 10.3934/mbe.2024020

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Abstract

In this paper, we studied the stability of traveling wave solutions of a two-species Lotka-Volterra 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.

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