In this paper, we study the existence of invasion waves of a diffusive predator–prey model with two preys and one predator. The existence of traveling semi-fronts connecting invasion-free equilibrium with wave speed [Formula: see text] is obtained by Schauder’s fixed-point theorem, where [Formula: see text] is the minimal wave speed. The boundedness of such waves is shown by rescaling method and such waves are proved to connect coexistence equilibrium by LaSalle’s invariance principle. The existence of traveling front with wave speed [Formula: see text] is got by rescaling method and limit arguments. The non-existence of traveling fronts with speed [Formula: see text] is shown by Laplace transform.

中文翻译：

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具有两个猎物和一个捕食者的扩散捕食者 - 猎物模型的入侵波

在本文中，我们研究了具有两个猎物和一个捕食者的扩散捕食者 - 猎物模型的入侵波的存在。由Schauder不动点定理得到连接无侵入平衡与波速的行进半锋的存在[公式：见正文]，其中[公式：见正文]为最小波速。这种波的有界性用重标度法表示，并用拉萨尔不变原理证明了这种波连接共存平衡。波速行进波的存在[公式：见正文]是通过重新标度法和极限参数得到的。拉普拉斯变换表明不存在高速行进[公式：见正文]。