Geodesic
Stability of Traveling Wavefronts for a Two-Component Lattice Dynamical System Arising in Competition Models
Canadian mathematical bulletin, Tome 61 (2018) no. 2, pp. 423-437

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DOI

In this paper, we study a two-component Lotka–Volterra competition systemon a one-dimensional spatial lattice. By the comparison principle, together with the weighted energy, we prove that the traveling wavefronts with large speed are exponentially asymptotically stable, when the initial perturbation around the traveling wavefronts decays exponentially as $j\,+\,ct\,\to \,-\,\infty $ , where $j\,\in \,\mathbb{Z}$ , $t\,>\,0$ , but the initial perturbation can be arbitrarily large on other locations. This partially answers an open problem by J.-S. Guo and C.-H.Wu.
DOI : 10.4153/CMB-2017-018-5
Mots-clés : 34A33, 34K20, 92D25, lattice dynamical system, competition model, traveling wavefront, stability 
Zhang, Guo-Bao; Tian, Ge. Stability of Traveling Wavefronts for a Two-Component Lattice Dynamical System Arising in Competition Models. Canadian mathematical bulletin, Tome 61 (2018) no. 2, pp. 423-437. doi: 10.4153/CMB-2017-018-5
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     author = {Zhang, Guo-Bao and Tian, Ge},
     title = {Stability of {Traveling} {Wavefronts} for a {Two-Component} {Lattice} {Dynamical} {System} {Arising} in {Competition} {Models}},
     journal = {Canadian mathematical bulletin},
     pages = {423--437},
     year = {2018},
     volume = {61},
     number = {2},
     doi = {10.4153/CMB-2017-018-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-018-5/}
}
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