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# Stability of Traveling Wavefronts for a Two-Component Lattice Dynamical System Arising in Competition Models

Published:2017-05-29
Printed: Jun 2018
• Guo-Bao Zhang,
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, People's Republic of China
• Ge Tian,
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, People's Republic of China
 Format: LaTeX MathJax PDF

## Abstract

In this paper, we study a two-component Lotka-Volterra competition system on an one-dimensional spatial lattice. By the method of 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 $j+ct \rightarrow -\infty$, where $j\in\mathbb{Z}$, $t\gt 0$, 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.
 Keywords: lattice dynamical system, competition model, traveling wavefront, stability
 MSC Classifications: 34A33 - Lattice differential equations 34K20 - Stability theory 92D25 - Population dynamics (general)

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