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

  • 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
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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 lattice dynamical system, competition model, traveling wavefront, stability
MSC Classifications: 34A33, 34K20, 92D25 show english descriptions Lattice differential equations
Stability theory
Population dynamics (general)
34A33 - Lattice differential equations
34K20 - Stability theory
92D25 - Population dynamics (general)
 

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