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

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

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.

Citation

Franco, D., Guiver, C., Logemann, H., & Perán, J. (2024). Persistency and stability of a class of nonlinear forced positive discrete-time systems with delays. Physica D: Nonlinear Phenomena, 467, Article 134260. https://doi.org/10.1016/j.physd.2024.134260

• Journal Article Type: Article
• Acceptance Date: Jun 11, 2024
• Online Publication Date: Jun 14, 2024
• Publication Date: 2024-11
• Deposit Date: Jun 11, 2024
• Publicly Available Date: Jun 11, 2024
• Print ISSN: 0167-2789
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 467
• Article Number: 134260
• 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