This article is concerned with the existence of traveling wave solutions for a discrete diffusive ratio-dependent predator-prey model. By applying Schauder’s fixed point theorem with the help of suitable upper and lower solutions, we prove that there exists a positive constant c * such that when c > c *, the discrete diffusive predator-prey system admits an invasion traveling wave. The existence of an invasion traveling wave with c = c * is also established by a limiting argument and a delicate analysis of the boundary conditions. Finally, by the asymptotic spreading theory and the comparison principle, the non-existence of invasion traveling waves with speed c < c * is also proved.

中文翻译：

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离散扩散比相关捕食者-猎物模型的入侵行波

本文关注离散扩散比相关捕食者-猎物模型行波解的存在性。通过应用 Schauder 不动点定理，借助合适的上下解，我们证明存在正常数 c * 使得当 c > c * 时，离散扩散捕食 - 猎物系统承认入侵行波。c = c * 的入侵行波的存在也是通过限制论证和对边界条件的精细分析来确定的。最后，通过渐近传播理论和比较原理，也证明了速度c < c * 的入侵行波不存在。