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Zhao, G. and Ruan, S. (2011) Existence, Uniqueness and Asymptotic Stability of Time Periodic Traveling Waves for a Periodic Lotka-Volterra Competition System with Diffusion. Journal de Mathématiques Pures et Appliquées, 95, 627-671.
https://doi.org/10.1016/j.matpur.2010.11.005

has been cited by the following article:

• TITLE: Propagation Dynamics of Forced Pulsating Waves for a Time Periodic Lotka-Volterra Cooperative System with Nonlocal Effects in Shifting Habitats

  AUTHORS: Zewen Gong

  KEYWORDS: Nonlocal Effects, Time Periodic Lotka-Volterra System, Forced Pulsating Waves, Shifting Habitats

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.10, October 21, 2024

  ABSTRACT: In this paper, we will concern the existence, asymptotic behaviors and stability of forced pulsating waves for a Lotka-Volterra cooperative system with nonlocal effects under shifting habitats. By using the alternatively-coupling upper-lower solution method, we establish the existence of forced pulsating waves, as long as the shifting speed falls in a finite interval where the endpoints are obtained from KPP-Fisher speeds. The asymptotic behaviors of the forced pulsating waves are derived. Finally, with proper initial, the stability of the forced pulsating waves is studied by the squeezing technique based on the comparison principle.