In this paper, we first establish the existence of semi-traveling wave solutions to a diffusive generalized Holling-Tanner predator-prey model in which the functional response may depend on both the predator and prey populations. Then, by constructing the Lyapunov function, we apply the obtained result to show the existence of traveling wave solutions to the diffusive Holling-Tanner predator-prey models with various functional responses, including the Lotka-Volterra type functional response, the Holling type Ⅱ functional response and the Beddington-DeAngelis functional response.

中文翻译：

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具扩散Holling-Tanner捕食者-食饵模型的行波解

在本文中，我们首先建立了一个弥散型广义Holling-Tanner捕食者-被捕食者模型的半行波解的存在，在该模型中，功能响应可能同时取决于捕食者和被捕食者的种群。然后，通过构造Lyapunov函数，我们将获得的结果用于说明具有多种功能响应的扩散Holling-Tanner捕食者－食饵模型的行波解的存在，包括Lotka-Volterra型功能性响应，HollingⅡ型功能反应和Beddington-DeAngelis功能反应。