Persistence and global attractivity in the model $A_{n+1}=A_nF(A_{n-m})$

TL;DR

This paper analyzes the persistence and attractivity of a discrete population model with delay, extending previous results to non-monotone functions and examining the impact of delay on system dynamics.

Contribution

It systematizes earlier results on uniform persistence and investigates the effect of delay in non-monotone cases using omega-limit sets.

Findings

Extended the understanding of persistence in delayed population models.

Analyzed the influence of delay on system stability and attractivity.

Utilized omega-limit set theory to study long-term behavior.

Abstract

First, we systemize ealier results the uniform persistence for discrete model $A_{n+1}=A_nF(A_{n-m})$ of population growth, where $F:(0,\infty)\to(0,\infty)$ is continuous and strictly decreasing. Second, we investigation the effect of delay $m$ when $F$ is not monotone. We are mainly using $\omega$-limit set of persistent solution, which is discussed in more general by P. Walters, 1982.