This paper focuses on traveling wave solutions for the so-called Rosenzweig–MacArthur predator–prey model with spatial diffusion. The main results of this note are concerned with the existence and uniqueness of traveling wave solution as well as periodic wave train solution in the large wave speed asymptotic. Depending on the model parameters we more particularly study the existence and uniqueness of a traveling wave connecting two equilibria or connecting an equilibrium point and a periodic wave train. We also discuss the existence and uniqueness of such a periodic wave train. Our analysis is based on ordinary differential equation techniques by coupling the theories of invariant manifolds together with those of global attractors.

本文关注于具有空间扩散的所谓Rosenzweig–MacArthur捕食者–被捕食模型的行波解。该注释的主要结果与行波解以及周期波列解在大波速渐近中的存在和唯一性有关。根据模型参数，我们更具体地研究连接两个平衡点或连接平衡点和周期波列的行波的存在和唯一性。我们还将讨论这种周期性波列的存在和唯一性。我们的分析是基于常微分方程技术，将不变流形的理论与整体吸引子的理论耦合在一起。