On Stability for Impulsive Delay Differential Equations and Application to a Periodic Lasota-Wazewska Model

TL;DR

This paper establishes new criteria for the global stability of impulsive delay differential equations, including periodic solutions, with applications to a generalized Lasota-Wazewska model featuring impulses and multiple delays.

Contribution

It relaxes traditional impulse conditions and applies stability analysis to complex periodic models with multiple delays.

Findings

Criteria for global stability of zero solutions established

Global attractivity of positive periodic solutions demonstrated

Applicable to complex biological delay models

Abstract

We consider a class of scalar delay differential equations with impulses and satisfying an Yorke-type condition, for which some criteria for the global stability of the zero solution are established. Here, the usual requirements about the impulses are relaxed. The results can be applied to study the stability of other solutions, such as periodic solutions. As an illustration, a very general periodic Lasota-Wazewska model with impulses and multiple time-dependent delays is addressed, and the global attractivity of its positive periodic solution analysed. Our results are discussed within the context of recent literature.