Traveling Wave Solutions For A Singular Diffusive Prey-Predator Model With Nonlocal Dispersal

TL;DR

This paper investigates traveling wave solutions in a singular diffusive prey-predator model with nonlocal dispersal, establishing existence and characterizing the range of admissible wave speeds.

Contribution

It introduces a novel analysis of traveling waves in a singular prey-predator system with nonlocal dispersal, including the characterization of wave speed intervals.

Findings

Existence of positive traveling wave solutions connecting predator-free and coexistence states.

Admissible wave speeds form a semi-infinite interval starting from a positive minimum.

Wave speed characterized by a variational formula.

Abstract

We study a singular diffusive prey-predator system with nonlocal dispersal for which the carrying capacity of the predator is proportional to the density of prey. We show the existence of positive one-dimensional traveling waves connecting the predator-free state and the constant co-existence state. The set of admissible wave speeds is proved to be equal to the semi-infinite interval $[s^*,\infty)$, for some $s^*>0$ which is characterized by a variational formula.