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

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.