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The exponential ordering for nonautonomous delay systems with applications to compartmental Nicholson systems

Part of: Smooth dynamical systems: general theory

Published online by Cambridge University Press:  27 March 2023

Sylvia Novo Open the ORCID record for Sylvia Novo [Opens in a new window] ,
Rafael Obaya Open the ORCID record for Rafael Obaya [Opens in a new window] ,
Ana M. Sanz Open the ORCID record for Ana M. Sanz [Opens in a new window]  and
Víctor M. Villarragut Open the ORCID record for Víctor M. Villarragut [Opens in a new window]
Sylvia Novo
Affiliation:
Departamento de Matemática Aplicada, Escuela de Ingenierías Industriales (Sede Doctor Mergelina), Universidad de Valladolid, 47011 Valladolid, Spain (sylvia.novo@uva.es)
Rafael Obaya
Affiliation:
Departamento de Matemática Aplicada, Escuela de Ingenierías Industriales (Sede Doctor Mergelina), Universidad de Valladolid, 47011 Valladolid, Spain, and Instituto de Investigación en Matemáticas, Universidad de Valladolid, Valladolid, Spain (rafael.obaya@uva.es)
Ana M. Sanz
Affiliation:
Instituto de Investigación en Matemáticas, Universidad de Valladolid, Valladolid, Spain, and Departamento de Didáctica de las Ciencias Experimentales, Sociales y de la Matemática, Facultad de Educación, Universidad de Valladolid, 34004 Palencia, Spain (anamaria.sanz@uva.es)
Víctor M. Villarragut
Affiliation:
Departamento de Matemática Aplicada a la Ingeniería Industrial, Universidad Politécnica de Madrid, Calle de José Gutiérrez Abascal 2, 28006 Madrid, Spain (victor.munoz@upm.es)
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Abstract

The exponential ordering is exploited in the context of nonautonomous delay systems, inducing monotone skew-product semiflows under less restrictive conditions than usual. Some dynamical concepts linked to the order, such as semiequilibria, are considered for the exponential ordering, with implications for the determination of the presence of uniform persistence or the existence of global attractors. Also, some important conclusions on the long-term dynamics and attraction are obtained for monotone and sublinear delay systems for this ordering. The results are then applied to almost periodic Nicholson systems and new conditions are given for the existence of a unique almost periodic positive solution which asymptotically attracts every other positive solution.

Keywords

nonautonomous dynamical systemsexponential orderinguniform persistenceglobal attractoralmost periodic Nicholson systems

MSC classification

Primary: 37C60: Nonautonomous smooth dynamical systems
Secondary: 37C65: Monotone flows 37C75: Stability theory 92D25: Population dynamics (general)
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 154 , Issue 2 , April 2024 , pp. 568 - 599
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Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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