Dynamics Beyond Bounds: (ω,c)-Periodic Functions and Their Impact on Delayed Population Models on Time Scales
Abstract
This paper delves into the study of (ω,c)-periodic functions on time scales that incorporate periodic, anti-periodic, Bloch, and certain unbounded functions. We examine several fundamental properties of this class of functions on translation-invariant time scales. We establish a suitable norm to equip this set of functions with a comprehensive mathematical framework. As a significant application of our theoretical findings, we investigate the unique existence of asymptotically exponentially stable (ω,c)-periodic solutions for some families of generalized dynamic equations on time scales incorporating feedback and time-varying delays representing population models. Our study specifically outlines sufficient conditions for the existence of (ω,c)-periodic solutions for some prominent models, such as the Nicholson model, the Lasota-Ważewska model, and their mixed versions on time scales. We provide some numerical examples and simulations to support our results. Our investigations are groundbreaking, encompassing discrete and continuous cases, providing a unified perspective on the (ω,c)-periodic behavior of various systems.
Recommended Citation
P. Bharti et al., "Dynamics Beyond Bounds: (ω,c)-Periodic Functions and Their Impact on Delayed Population Models on Time Scales," Discrete and Continuous Dynamical Systems Series S, vol. 18, no. 9, pp. 2586 - 2621, American Institute of Mathematical Sciences, Sep 2025.
The definitive version is available at https://doi.org/10.3934/dcdss.2025049
Department(s)
Mathematics and Statistics
Keywords and Phrases
(ω,c)-periodicity; exponential stability; Lasota-Ważewska model; Nicholson model; population models; time scale calculus; time-varying delays
International Standard Serial Number (ISSN)
1937-1179; 1937-1632
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2025 American Institute of Mathematical Sciences, All rights reserved.
Publication Date
01 Sep 2025
