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Persistency and stability of a class of nonlinear forced positive discrete-time systems with delays

Franco, Daniel; Guiver, Chris; Logemann, Hartmut; Peran, Juan

Authors

Daniel Franco

Hartmut Logemann

Juan Peran



Abstract

Persistence, excitability and stability properties are considered for a class of nonlinear, forced, positive discrete-time systems with delays. As will be illustrated, these equations arise in a number of biological and ecological contexts. Novel sufficient conditions for persistence, excitability and stability are presented. Further, similarities and differences between the delayed equations considered presently and their corresponding undelayed versions are explored, and some striking differences are noted. It is shown that recent results for a corresponding class of positive, nonlinear delay-differential (continuous-time) systems do not carry over to the discrete-time setting. Detailed discussion of three examples from population dynamics is provided.

Journal Article Type Article
Acceptance Date Jun 11, 2024
Online Publication Date Jun 14, 2024
Deposit Date Jun 11, 2024
Publicly Available Date Jun 14, 2024
Print ISSN 0167-2789
Publisher Elsevier
Peer Reviewed Peer Reviewed
DOI https://doi.org/10.1016/j.physd.2024.134260
Keywords Difference equation, excitability, Lur’e system, persistence, positive system, stability, time delay
Publisher URL https://www.sciencedirect.com/journal/physica-d-nonlinear-phenomena

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Persistency and stability of a class of nonlinear forced positive discrete-time systems with delays (accepted version) (775 Kb)
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