On persistence of a Nicholson-type system with multiple delays and nonlinear harvesting

TL;DR

This paper studies an N-dimensional Nicholson-type system with multiple delays and nonlinear harvesting, establishing conditions for persistence, existence of periodic solutions, and global stability of zero.

Contribution

It extends Nicholson's equation to multiple delays and nonlinear terms, providing new conditions for persistence and periodic solutions.

Findings

Conditions for strong and uniform persistence established

Existence of T-periodic solutions proven under certain hypotheses

Zero is shown to be a global attractor under reversed conditions

Abstract

An N-dimensional generalization of Nicholson's equation is analyzed. We consider a model including multiple delays, nonlinear coefficients and a nonlinear harvesting term. Inspired by previous results in this subject, we obtain sufficient conditions to guarantee strong and uniform persistence. Furthermore, under extra suitable hypotheses we prove the existence of T-periodic solutions and, reversing the prior conditions in a convenient manner, we show that the zero is a global attractor.