Positive periodic solutions for systems of impulsive delay differential equations

TL;DR

This paper establishes criteria for the existence of positive periodic solutions in complex impulsive delay differential systems, with applications to biological models like hematopoiesis and Nicholson systems.

Contribution

It extends previous scalar results to multidimensional systems with general nonlinearities and impulses, providing new existence criteria.

Findings

Criteria for positive periodic solutions are derived.

Applications to biological models demonstrate practical relevance.

Results generalize previous scalar case findings.

Abstract

A class of periodic differential $n$-dimensional systems with patch structure with (possibly infinite) delay and nonlinear impulses is considered. These systems incorporate very general nonlinearities and impulses whose signs may vary. Criteria for the existence of at least one positive periodic solution are presented, extending and improving previous ones established for the scalar case. Applications to systems inspired in mathematical biology models, such as impulsive hematopoiesis and Nicholson-type systems, are also included.