Permanence for nonautonomous differential systems with delays in the linear and nonlinear terms

TL;DR

This paper establishes conditions ensuring the long-term persistence of nonautonomous delay differential systems, including biological models with complex delays and nonmonotone nonlinearities, broadening understanding of their stability and permanence.

Contribution

It provides new sufficient conditions for permanence in nonautonomous delay systems with nonmonotone nonlinearities, applicable to biological models like Nicholson and Mackey-Glass systems.

Findings

Derived explicit permanence conditions for complex delay systems

Applied results to biological models demonstrating long-term persistence

Extended existing theories to nonautonomous, nonmonotone systems

Abstract

In this paper, we obtain sufficient conditions for the permanence of a family of nonautonomous systems of delay differential equations. This family includes structured models from mathematical biology, with either discrete or distributed delays in both the linear and nonlinear terms, and where typically the nonlinear terms are nonmonotone. Applications to generalized Nicholson or Mackey-Glass systems are given.