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Boundedness, persistence and stability for classes of forced difference equations arising in population ecology

Boundedness, persistence and stability properties are considered for a class of nonlinear, possibly infinite-dimensional, forced difference equations which arise in a number of ecological and biological contexts. The inclusion of forcing incorporates the effects of control actions (such as harvestin...

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Autores principales: Franco, D., Guiver, C., Logemann, H., Perán, J.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2019
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6667429/
https://www.ncbi.nlm.nih.gov/pubmed/31168636
http://dx.doi.org/10.1007/s00285-019-01388-7
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author Franco, D.
Guiver, C.
Logemann, H.
Perán, J.
author_facet Franco, D.
Guiver, C.
Logemann, H.
Perán, J.
author_sort Franco, D.
collection PubMed
description Boundedness, persistence and stability properties are considered for a class of nonlinear, possibly infinite-dimensional, forced difference equations which arise in a number of ecological and biological contexts. The inclusion of forcing incorporates the effects of control actions (such as harvesting or breeding programmes), disturbances induced by seasonal or environmental variation, or migration. We provide sufficient conditions under which the states of these models are bounded and persistent uniformly with respect to the forcing terms. Under mild assumptions, the models under consideration naturally admit two equilibria when unforced: the origin and a unique non-zero equilibrium. We present sufficient conditions for the non-zero equilibrium to be stable in a sense which is strongly inspired by the input-to-state stability concept well-known in mathematical control theory. In particular, our stability concept incorporates the impact of potentially persistent forcing. Since the underlying state-space may be infinite dimensional, our framework enables treatment of so-called integral projection models (IPMs). The theory is applied to a number of examples from population dynamics.
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spelling pubmed-66674292019-08-14 Boundedness, persistence and stability for classes of forced difference equations arising in population ecology Franco, D. Guiver, C. Logemann, H. Perán, J. J Math Biol Article Boundedness, persistence and stability properties are considered for a class of nonlinear, possibly infinite-dimensional, forced difference equations which arise in a number of ecological and biological contexts. The inclusion of forcing incorporates the effects of control actions (such as harvesting or breeding programmes), disturbances induced by seasonal or environmental variation, or migration. We provide sufficient conditions under which the states of these models are bounded and persistent uniformly with respect to the forcing terms. Under mild assumptions, the models under consideration naturally admit two equilibria when unforced: the origin and a unique non-zero equilibrium. We present sufficient conditions for the non-zero equilibrium to be stable in a sense which is strongly inspired by the input-to-state stability concept well-known in mathematical control theory. In particular, our stability concept incorporates the impact of potentially persistent forcing. Since the underlying state-space may be infinite dimensional, our framework enables treatment of so-called integral projection models (IPMs). The theory is applied to a number of examples from population dynamics. Springer Berlin Heidelberg 2019-06-06 2019 /pmc/articles/PMC6667429/ /pubmed/31168636 http://dx.doi.org/10.1007/s00285-019-01388-7 Text en © The Author(s) 2019 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Franco, D.
Guiver, C.
Logemann, H.
Perán, J.
Boundedness, persistence and stability for classes of forced difference equations arising in population ecology
title Boundedness, persistence and stability for classes of forced difference equations arising in population ecology
title_full Boundedness, persistence and stability for classes of forced difference equations arising in population ecology
title_fullStr Boundedness, persistence and stability for classes of forced difference equations arising in population ecology
title_full_unstemmed Boundedness, persistence and stability for classes of forced difference equations arising in population ecology
title_short Boundedness, persistence and stability for classes of forced difference equations arising in population ecology
title_sort boundedness, persistence and stability for classes of forced difference equations arising in population ecology
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6667429/
https://www.ncbi.nlm.nih.gov/pubmed/31168636
http://dx.doi.org/10.1007/s00285-019-01388-7
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