Forced waves and their asymptotic behaviors in a Lotka-Volterra competition model with spatio-temporal nonlocal effect under climate change

Yong Yang; Zunxian Li; Chengyi Xia; Yong Yang; Zunxian Li; Chengyi Xia

doi:10.3934/mbe.2023608

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 8: 13638-13659. doi: 10.3934/mbe.2023608

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Research article

Forced waves and their asymptotic behaviors in a Lotka-Volterra competition model with spatio-temporal nonlocal effect under climate change

1.
School of Mathematics and Big Data, Foshan University, Foshan 528000, China
2.
Department of Mathematics, Tianjin University of Technology, Tianjin 300384, China
3.
School of Artificial Intelligence, Tiangong University, Tianjin 300387, China

Received: 03 April 2023 Revised: 28 May 2023 Accepted: 01 June 2023 Published: 14 June 2023

In this paper, we propose a modified Lotka-Volterra competition model under climate change, which incorporates both spatial and temporal nonlocal effect. First, the theoretical analyses for forced waves of the model are performed, and the existence of the forced waves is proved by using the cross-iteration scheme combining with appropriate upper and lower solutions. Second, the asymptotic behaviors of the forced waves are derived by using the linearization and limiting method, and we find that the asymptotic behaviors of forced waves are mainly determined by the leading equations. In addition, some typical numerical examples are provided to illustrate the analytical results. By choosing three kinds of different kernel functions, it is found that the forced waves can be both monotonic and non-monotonic.
- nonlocal effect,
- forced wave,
- competitive system,
- climate change
Citation: Yong Yang, Zunxian Li, Chengyi Xia. Forced waves and their asymptotic behaviors in a Lotka-Volterra competition model with spatio-temporal nonlocal effect under climate change[J]. Mathematical Biosciences and Engineering, 2023, 20(8): 13638-13659. doi: 10.3934/mbe.2023608

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Abstract

In this paper, we propose a modified Lotka-Volterra competition model under climate change, which incorporates both spatial and temporal nonlocal effect. First, the theoretical analyses for forced waves of the model are performed, and the existence of the forced waves is proved by using the cross-iteration scheme combining with appropriate upper and lower solutions. Second, the asymptotic behaviors of the forced waves are derived by using the linearization and limiting method, and we find that the asymptotic behaviors of forced waves are mainly determined by the leading equations. In addition, some typical numerical examples are provided to illustrate the analytical results. By choosing three kinds of different kernel functions, it is found that the forced waves can be both monotonic and non-monotonic.

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