English

Traveling Wave in a Ratio-dependent Holling-Tanner System with Nonlocal Diffusion and Strong Allee Effect

Analysis of PDEs 2023-06-02 v1 Dynamical Systems

Abstract

In this paper, a ratio-dependent Holling-Tanner system with nonlocal diffusion is taken into account, where the prey is subject to a strong Allee effect. To be special, by applying Schauder's fixed point theorem and iterative technique, we provide a general theory on the existence of traveling waves for such system. Then appropriate upper and lower solutions and a novel sequence, similar to squeeze method, are constructed to demonstrate the existence of traveling waves for c>c*. Moreover, the existence of traveling wave for c=c* is also established by spreading speed theory and comparison principle. Finally, the nonexistence of traveling waves for c<c* is investigated, and the minimal wave speed then is determined.

Keywords

Cite

@article{arxiv.2306.00666,
  title  = {Traveling Wave in a Ratio-dependent Holling-Tanner System with Nonlocal Diffusion and Strong Allee Effect},
  author = {Hongliang Li and Min Zhao and Rong Yuan},
  journal= {arXiv preprint arXiv:2306.00666},
  year   = {2023}
}