Dynamic properties of a class of forced positive higher-order scalar difference equations: persistency, stability and convergence

Daniel Franco; Chris Guiver; Hartmut Logemann; Juan Perán

doi:10.1080/10236198.2025.2461530

Dynamic properties of a class of forced positive higher-order scalar difference equations: persistency, stability and convergence

Daniel Franco, Chris Guiver, Hartmut Logemann, Juan Perán

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

Persistency, stability and convergence properties are considered for a class of nonlinear, forced, positive, scalar higher-order difference equations. Sufficient conditions for these properties to hold are derived, broadly in terms of the interplay of the linear and nonlinear components of the difference equations. The convergence results presented include asymptotic response properties when the system is subject to (asymptotically) almost periodic forcing. The equations under consideration arise in a number of ecological and biological contexts, with the Allen-Clark population model appearing as a special case. We illustrate our results by several examples from population dynamics.

Original language	English
Number of pages	35
Journal	Journal of Difference Equations and Applications
Early online date	17 Feb 2025
DOIs	https://doi.org/10.1080/10236198.2025.2461530
Publication status	E-pub ahead of print - 17 Feb 2025

Data Availability Statement

Data sharing is not applicable to this article as no new data were created or analysed in this study.

Keywords

Allen-Clark model
almost periodic forcing
difference equation
persistence
positive Lur'e system
stability

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Applied Mathematics

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10.1080/10236198.2025.2461530Licence: CC BY-NC-ND

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abstract = "Persistency, stability and convergence properties are considered for a class of nonlinear, forced, positive, scalar higher-order difference equations. Sufficient conditions for these properties to hold are derived, broadly in terms of the interplay of the linear and nonlinear components of the difference equations. The convergence results presented include asymptotic response properties when the system is subject to (asymptotically) almost periodic forcing. The equations under consideration arise in a number of ecological and biological contexts, with the Allen-Clark population model appearing as a special case. We illustrate our results by several examples from population dynamics.",

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T2 - persistency, stability and convergence

AU - Franco, Daniel

AU - Guiver, Chris

AU - Logemann, Hartmut

AU - Perán, Juan

PY - 2025/2/17

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N2 - Persistency, stability and convergence properties are considered for a class of nonlinear, forced, positive, scalar higher-order difference equations. Sufficient conditions for these properties to hold are derived, broadly in terms of the interplay of the linear and nonlinear components of the difference equations. The convergence results presented include asymptotic response properties when the system is subject to (asymptotically) almost periodic forcing. The equations under consideration arise in a number of ecological and biological contexts, with the Allen-Clark population model appearing as a special case. We illustrate our results by several examples from population dynamics.

AB - Persistency, stability and convergence properties are considered for a class of nonlinear, forced, positive, scalar higher-order difference equations. Sufficient conditions for these properties to hold are derived, broadly in terms of the interplay of the linear and nonlinear components of the difference equations. The convergence results presented include asymptotic response properties when the system is subject to (asymptotically) almost periodic forcing. The equations under consideration arise in a number of ecological and biological contexts, with the Allen-Clark population model appearing as a special case. We illustrate our results by several examples from population dynamics.

KW - Allen-Clark model

KW - almost periodic forcing

KW - difference equation

KW - persistence

KW - positive Lur'e system

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Dynamic properties of a class of forced positive higher-order scalar difference equations: persistency, stability and convergence

Abstract

Data Availability Statement

Keywords

ASJC Scopus subject areas

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