Electron. J. Differential Equations, Vol. 2020 (2020), No. 88, pp. 1-17.

Existence and stability of traveling waves for a competitive-cooperative recursion system

Xiongxiong Bao, Ting Li

Abstract:
This article concerns the existence and global stability of bistable traveling waves for a competitive-cooperative recursion system. We first show that the spatially homogeneous system associated with the competitive-cooperative recursion system admits a bistable structure. Then using the theory of bistable waves for monotone semiflows and a dynamical system approach, we prove that there exists an unique and global stable traveling wave solution connecting two stable equilibria for such recursion system under appropriate conditions.

Submitted September 19, 2019. Published August 17, 2020.
Math Subject Classifications: 45G15, 45M10, 92D25.
Key Words: Existence; global stability; traveling waves; competitive-cooperative recursion system.
DOI: 10.58997/ejde.2020.88

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Xiongxiong Bao
School of Science
Chang'an University
Xi'an, Shaanxi 710064, China
email: baoxx2016@chd.edu.cn
Ting Li
School of Mathematics and Statistics
Lanzhou University
Lanzhou, Gansu 730000, China
email: liting2017@lzu.edu.cn

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