Global stability of traveling wave fronts in a two-dimensional lattice dynamical system with global interaction

Cui-Ping Cheng; Ruo-Fan An; Cui-Ping Cheng; Ruo-Fan An

doi:10.3934/era.2021051

Electronic Research Archive

2021, Volume 29, Issue 5: 3535-3550. doi: 10.3934/era.2021051

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Global stability of traveling wave fronts in a two-dimensional lattice dynamical system with global interaction

Cui-Ping Cheng ^{1
,
,},
Ruo-Fan An ^{2
,}

1.
School of Science, Shanghai Institute of Technology, Shanghai 201418, China
2.
School of Mathematics, University of Mining and Technology, Xuzhou, Jiangsu 221008, China

Received: 01 February 2021 Revised: 01 May 2021 Published: 22 July 2021
35B40, 35K57, 35R20

This paper is concerned with the traveling wave fronts for a lattice dynamical system with global interaction, which arises in a single species in a 2D patchy environment with infinite number of patches connected locally by diffusion and global interaction by delay. We prove that all non-critical traveling wave fronts are globally exponentially stable in time, and the critical traveling wave fronts are globally algebraically stable by the weighted energy method combined with the comparison principle and the discrete Fourier transform.
- Lattice differential equation with global interaction,
- global stability,
- weighted energy method,
- comparison principle,
- discrete Fourier transform
Citation: Cui-Ping Cheng, Ruo-Fan An. Global stability of traveling wave fronts in a two-dimensional lattice dynamical system with global interaction[J]. Electronic Research Archive, 2021, 29(5): 3535-3550. doi: 10.3934/era.2021051

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Abstract

This paper is concerned with the traveling wave fronts for a lattice dynamical system with global interaction, which arises in a single species in a 2D patchy environment with infinite number of patches connected locally by diffusion and global interaction by delay. We prove that all non-critical traveling wave fronts are globally exponentially stable in time, and the critical traveling wave fronts are globally algebraically stable by the weighted energy method combined with the comparison principle and the discrete Fourier transform.

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