Title:	The Beverton–Hold model on isolated time scales
Authors:	Bohner, Martin Mesquita, Jaqueline Godoy Streipert, Sabrina
metadata.dc.contributor.email:	mailto:bohner@mst.edu
Assunto::	Equações de Beverton–Holt Conjectura de Cushing-Henson Escala de tempo isolada
Issue Date:	15-Aug-2022
Publisher:	AIMS
Citation:	BOHNER, Martin; MESQUITA, Jaqueline; STREIPERT, Sabrina. The Beverton–Hold model on isolated time scales. Mathematical Biosciences and Engineering, Springfield, v. 19, n. 11, p. 11693-11716, 2022. DOI 10.3934/mbe.2022544. Disponível em: https://www.aimspress.com/article/id/62fa2d9eba35de77c348a1ef. Acesso em: 26 set. 2022.
Abstract:	In this work, we formulate the Beverton–Holt model on isolated time scales and extend existing results known in the discrete and quantum calculus cases. Applying a recently introduced definition of periodicity for arbitrary isolated time scales, we discuss the effects of periodicity onto a population modeled by a dynamic version of the Beverton–Holt equation. The first main theorem provides conditions for the existence of a unique ω-periodic solution that is globally asymptotically stable, which addresses the first Cushing–Henson conjecture on isolated time scales. The second main theorem concerns the generalization of the second Cushing–Henson conjecture. It investigates the effects of periodicity by deriving an upper bound for the average of the unique periodic solution. The obtained upper bound reveals a dependence on the underlying time structure, not apparent in the classical case. This work also extends existing results for the Beverton–Holt model in the discrete and quantum cases, and it complements existing conclusions on periodic time scales. This work can furthermore guide other applications of the recently introduced periodicity on isolated time scales.
Licença::	Mathematical Biosciences and Engineering - All articles published by AIMS Press are Open Access under the Creative Commons Attribution License ( http://creativecommons.org/licenses/by/4.0 ). Under this license, authors retain ownership of the copyright for their content, and anyone can copy, distribute, or reuse these articles as long as the author and original source are properly cited. Fonte: https://www.aimspress.com/index/news/solo-detail/openaccesspolicy. Acesso em: 26 set. 2022.
DOI:	https://doi.org/10.3934/mbe.2022544
Appears in Collections:	Artigos publicados em periódicos e afins

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