Periodic Traveling Waves in an Integro-Difference Equation With Non-Monotonic Growth and Strong Allee Effect

TL;DR

This paper establishes conditions for periodic traveling waves in an integro-difference model with non-monotonic growth and Allee effects, linking wave speed to population spread, with case studies on specific kernels.

Contribution

It provides new theoretical conditions for the existence of periodic traveling waves in complex growth models with Allee effects, including specific kernel analyses.

Findings

Existence of periodic traveling waves under certain conditions

Wave speed equals asymptotic spreading speed for compact initial data

Case studies on Laplace and uniform kernels

Abstract

We derive sufficient conditions for the existence of a periodic traveling wave solution to an integro-difference equation with a piecewise constant growth function exhibiting a stable period2 cycle and strong Allee effect. The mean traveling wave speed is shown to be the asymptotic spreading speed of solutions with compactly supported initial data under appropriate conditions. We then conduct case studies for the Laplace kernel and uniform kernel.