Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 88, pp. 1-17.

Title: Existence and stability of traveling waves for a competitive-cooperative
       recursion system 
       
Authors: Xiongxiong Bao (Chang'an Univ., Xi'an, Shaanxi, China)
         Ting Li (Lanzhou Univ., Lanzhou, Gansu, China)

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.