Blowing-up of deterministic fixed points in stochastic population dynamics

Autores
Natiello, Mario A.; Solari, Hernan Gustavo
Año de publicación
2007
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We discuss the stochastic dynamics of biological (and other) populations presenting a limit behaviour for large environments (called deterministic limit) and its relation with the dynamics in the limit. The discussion is circumscribed to linearly stable fixed points of the deterministic dynamics, and it is shown that the cases of extinction and non-extinction equilibriums present different features. Mainly, non-extinction equilibria have associated a region of stochastic instability surrounded by a region of stochastic stability. The instability region does not exist in the case of extinction fixed points, and a linear Lyapunov function can be associated with them. Stochastically sustained oscillations of two subpopulations are also discussed in the case of complex eigenvalues of the stability matrix of the deterministic system. © 2007 Elsevier Inc. All rights reserved.
Fil: Natiello, Mario A.. Lund University; Suecia
Fil: Solari, Hernan Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina
Materia
Deterministic Limit
Population Dynamics
Stochastic
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/67522
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Blowing-up of deterministic fixed points in stochastic population dynamicsNatiello, Mario A.Solari, Hernan GustavoDeterministic LimitPopulation DynamicsStochastichttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We discuss the stochastic dynamics of biological (and other) populations presenting a limit behaviour for large environments (called deterministic limit) and its relation with the dynamics in the limit. The discussion is circumscribed to linearly stable fixed points of the deterministic dynamics, and it is shown that the cases of extinction and non-extinction equilibriums present different features. Mainly, non-extinction equilibria have associated a region of stochastic instability surrounded by a region of stochastic stability. The instability region does not exist in the case of extinction fixed points, and a linear Lyapunov function can be associated with them. Stochastically sustained oscillations of two subpopulations are also discussed in the case of complex eigenvalues of the stability matrix of the deterministic system. © 2007 Elsevier Inc. All rights reserved.Fil: Natiello, Mario A.. Lund University; SueciaFil: Solari, Hernan Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaElsevier Science Inc2007-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/67522Natiello, Mario A.; Solari, Hernan Gustavo; Blowing-up of deterministic fixed points in stochastic population dynamics; Elsevier Science Inc; Mathematical Biosciences; 209; 2; 12-2007; 319-3350025-5564CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.mbs.2007.02.002info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:43:54Zoai:ri.conicet.gov.ar:11336/67522instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:43:54.284CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Blowing-up of deterministic fixed points in stochastic population dynamics
title Blowing-up of deterministic fixed points in stochastic population dynamics
spellingShingle Blowing-up of deterministic fixed points in stochastic population dynamics
Natiello, Mario A.
Deterministic Limit
Population Dynamics
Stochastic
title_short Blowing-up of deterministic fixed points in stochastic population dynamics
title_full Blowing-up of deterministic fixed points in stochastic population dynamics
title_fullStr Blowing-up of deterministic fixed points in stochastic population dynamics
title_full_unstemmed Blowing-up of deterministic fixed points in stochastic population dynamics
title_sort Blowing-up of deterministic fixed points in stochastic population dynamics
dc.creator.none.fl_str_mv Natiello, Mario A.
Solari, Hernan Gustavo
author Natiello, Mario A.
author_facet Natiello, Mario A.
Solari, Hernan Gustavo
author_role author
author2 Solari, Hernan Gustavo
author2_role author
dc.subject.none.fl_str_mv Deterministic Limit
Population Dynamics
Stochastic
topic Deterministic Limit
Population Dynamics
Stochastic
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We discuss the stochastic dynamics of biological (and other) populations presenting a limit behaviour for large environments (called deterministic limit) and its relation with the dynamics in the limit. The discussion is circumscribed to linearly stable fixed points of the deterministic dynamics, and it is shown that the cases of extinction and non-extinction equilibriums present different features. Mainly, non-extinction equilibria have associated a region of stochastic instability surrounded by a region of stochastic stability. The instability region does not exist in the case of extinction fixed points, and a linear Lyapunov function can be associated with them. Stochastically sustained oscillations of two subpopulations are also discussed in the case of complex eigenvalues of the stability matrix of the deterministic system. © 2007 Elsevier Inc. All rights reserved.
Fil: Natiello, Mario A.. Lund University; Suecia
Fil: Solari, Hernan Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina
description We discuss the stochastic dynamics of biological (and other) populations presenting a limit behaviour for large environments (called deterministic limit) and its relation with the dynamics in the limit. The discussion is circumscribed to linearly stable fixed points of the deterministic dynamics, and it is shown that the cases of extinction and non-extinction equilibriums present different features. Mainly, non-extinction equilibria have associated a region of stochastic instability surrounded by a region of stochastic stability. The instability region does not exist in the case of extinction fixed points, and a linear Lyapunov function can be associated with them. Stochastically sustained oscillations of two subpopulations are also discussed in the case of complex eigenvalues of the stability matrix of the deterministic system. © 2007 Elsevier Inc. All rights reserved.
publishDate 2007
dc.date.none.fl_str_mv 2007-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/67522
Natiello, Mario A.; Solari, Hernan Gustavo; Blowing-up of deterministic fixed points in stochastic population dynamics; Elsevier Science Inc; Mathematical Biosciences; 209; 2; 12-2007; 319-335
0025-5564
CONICET Digital
CONICET
url http://hdl.handle.net/11336/67522
identifier_str_mv Natiello, Mario A.; Solari, Hernan Gustavo; Blowing-up of deterministic fixed points in stochastic population dynamics; Elsevier Science Inc; Mathematical Biosciences; 209; 2; 12-2007; 319-335
0025-5564
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.mbs.2007.02.002
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science Inc
publisher.none.fl_str_mv Elsevier Science Inc
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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