In this paper, we present some recent developments on the application of Schauder’s fixed point theorem to the existence of traveling waves for some three-species predator-prey systems. The existence of traveling waves of predator-prey systems is closely related to the invasion phenomenon of some alien species to the habitat of aboriginal species. Three different three-species predator-prey models with different invaded and invading states are presented. In this paper, we focus on the methodology of deriving the convergence of stale tail of wave profiles.
