Global Stability of Traveling Waves for the Lotka–Volterra Competition System with Three Species

Shulin Hu, Chaohong Pan and Lin Wang ()
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Shulin Hu: School of Mathematics and Physics, University of South China, Hengyang 421001, China
Chaohong Pan: School of Mathematics and Physics, University of South China, Hengyang 421001, China
Lin Wang: Basic Department, Hunan Institute of Traffic Engineering, Hengyang 421001, China

Mathematics, 2023, vol. 11, issue 9, 1-14

Abstract: The stability of traveling waves for the Lotka–Volterra competition system with three species is investigated in this paper. Specifically, we first show the asymptotic behavior of traveling wave solutions and then establish the local stability and the global stability under the weighted functional space. For local stability, the spectrum approach is used, while for global stability, the comparison principle and squeezing theorem are combined.

Keywords: asymptotic behavior; Lotka–Volterra model; three species; global stability; weighted functional space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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