Global attractivity for a nonautonomous Nicholson's equation with mixed monotonicities

TL;DR

This paper establishes new criteria for the stability and attractivity of a nonautonomous Nicholson's equation with multiple delays and mixed monotonicity, improving upon recent results and addressing open problems.

Contribution

It provides novel sufficient conditions for permanence, local stability, and global attractivity in a complex delayed Nicholson's equation with mixed monotone nonlinearities.

Findings

Criteria depend on delay sizes and improve existing results.

Conditions ensure positive equilibrium stability and attractivity.

Addresses open problems in the stability analysis of such equations.

Abstract

We consider a Nicholson's equation with multiple pairs of time-varying delays and nonlinear terms given by mixed monotone functions. Sufficient conditions for the permanence, local stability and global attractivity of its positive equilibrium are established. Our criteria depend on the size of some delays, improve results in recent literature and provide answers to some open problems.