Is uniform persisitence a robust property in almost periodic models? A well-behaved family: almost periodic Nicholson systems

TL;DR

This paper investigates the robustness of uniform persistence in almost periodic Nicholson systems, revealing that persistence depends on the entire family of systems rather than individual models, due to non-robustness in almost periodic differential equations.

Contribution

It provides a complete characterization of persistence in almost periodic Nicholson systems using computable exponents, highlighting the collective nature of persistence in non-autonomous models.

Findings

Persistence is characterized by numerically computable exponents.

Uniform persistence is not robust in almost periodic differential equations.

Persistence depends on the entire family of systems over the hull.

Abstract

Using techniques of non-autonomous dynamical systems, we completely characterize the persistence properties of an almost periodic Nicholson system in terms of some numerically computable exponents. Although similar results hold for a class of cooperative and sublinear models, in the general non-autonomous setting one has to consider persistence as a collective property of the family of systems over the hull: the reason is that uniform persistence is not a robust property in models given by almost periodic differential equations.