Open AccessGlobal stability of traveling wave fronts in a two-dimensional lattice dynamical system with global interaction
Author(s) -
Cungui Cheng,
Ruo-fan An
Publication year - 2021
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2021051
Subject(s) - traveling wave , lattice (music) , fourier transform , physics , exponential growth , mathematical analysis , mathematics , statistical physics , acoustics
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.