Long-time behavior of a nonlocal dispersal logistic model with seasonal succession

TL;DR

This paper investigates a nonlocal dispersal logistic model with seasonal effects, establishing criteria for species persistence or extinction and analyzing the long-term behavior of the population in a bounded habitat.

Contribution

It introduces a novel persistence-extinction criterion for nonlocal models with seasonal succession, differing from local diffusion models, and characterizes the asymptotic profile of solutions.

Findings

Persistence-extinction criterion established

Asymptotic profile of positive solutions determined

Differences from local diffusion models highlighted

Abstract

This paper is devoted to a nonlocal dispersal logistic model with seasonal succession in one-dimensional bounded habitat, where the seasonal succession accounts for the effect of two different seasons. Firstly, we provide the persistence-extinction criterion for the species, which is different from that for local diffusion model. Then we show the asymptotic profile of the time-periodic positive solution as the species persists in long run.