Global stability in some one-dimensional non-autonomous discrete periodic population models

TL;DR

This paper extends the enveloping method to analyze global stability in one-dimensional periodic population models, demonstrating that individual enveloping can imply periodic enveloping under certain conditions.

Contribution

The paper introduces a novel extension of the enveloping method from autonomous to periodic models, establishing conditions for global stability analysis.

Findings

Extended enveloping method to periodic models

Established conditions for global stability in periodic models

Demonstrated equivalence of individual and periodic enveloping

Abstract

For some one-dimensional discrete-time autonomous population models, local stability implies global stability of the positive equilibrismo point. One of the known techniques is the enveloping method. In this paper we extend the enveloping method to one single periodic population models. We show that, under certain conditions, "individual enveloping" implies "periodic enveloping" in one-dimensional periodic population models.