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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

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

* Corresponding author: Cui-Ping Cheng

Received  February 2021 Revised  May 2021 Early access July 2021

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.

Citation: Cui-Ping Cheng, Ruo-Fan An. Global stability of traveling wave fronts in a two-dimensional lattice dynamical system with global interaction. Electronic Research Archive, doi: 10.3934/era.2021051
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