Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks

Bibliographic Details
Main Author: Faria, Teresa
Publication Date: 2008
Other Authors: Oliveira, José J.
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: https://hdl.handle.net/1822/8041
Summary: This paper addresses the local and global stability of n-dimensional Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks. Necessary and sufficient conditions for local stability independent of the choice of the delay functions are given, by imposing a weak nondelayed diagonal dominance which cancels the delayed competition effect. The global asymptotic stability of positive equilibria is established under conditions slightly stronger than the ones required for the linear stability. For the case of monotone interactions, however, sharper conditions are presented. This paper generalizes known results for discrete delays to systems with distributed delays. Several applications illustrate the results.
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spelling Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacksLotka-Volterra systemDelayed population modelDistributed delaysGlobal asymptotic stabilityLocal asymptotic stabilityInstantaneous negative feedbackScience & TechnologyThis paper addresses the local and global stability of n-dimensional Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks. Necessary and sufficient conditions for local stability independent of the choice of the delay functions are given, by imposing a weak nondelayed diagonal dominance which cancels the delayed competition effect. The global asymptotic stability of positive equilibria is established under conditions slightly stronger than the ones required for the linear stability. For the case of monotone interactions, however, sharper conditions are presented. This paper generalizes known results for discrete delays to systems with distributed delays. Several applications illustrate the results.Fundação para a Ciência e a Tecnologia (FCT) - programa POCI, projecto PDCT/ MAT/56476/2004.Portugal-FEDERElsevierUniversidade do MinhoFaria, TeresaOliveira, José J.2008-03-012008-03-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/8041eng"Journal of Differential Equations". ISSN 0022-0396. 244:5 (Mar. 2008) 1049-1079.0022-039610.1016/j.jde.2007.12.005http://www.sciencedirect.com/science/journal/00220396info:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2025-04-12T04:17:28Zoai:repositorium.sdum.uminho.pt:1822/8041Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T14:59:54.242137Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks
title Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks
spellingShingle Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks
Faria, Teresa
Lotka-Volterra system
Delayed population model
Distributed delays
Global asymptotic stability
Local asymptotic stability
Instantaneous negative feedback
Science & Technology
title_short Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks
title_full Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks
title_fullStr Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks
title_full_unstemmed Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks
title_sort Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks
author Faria, Teresa
author_facet Faria, Teresa
Oliveira, José J.
author_role author
author2 Oliveira, José J.
author2_role author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Faria, Teresa
Oliveira, José J.
dc.subject.por.fl_str_mv Lotka-Volterra system
Delayed population model
Distributed delays
Global asymptotic stability
Local asymptotic stability
Instantaneous negative feedback
Science & Technology
topic Lotka-Volterra system
Delayed population model
Distributed delays
Global asymptotic stability
Local asymptotic stability
Instantaneous negative feedback
Science & Technology
description This paper addresses the local and global stability of n-dimensional Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks. Necessary and sufficient conditions for local stability independent of the choice of the delay functions are given, by imposing a weak nondelayed diagonal dominance which cancels the delayed competition effect. The global asymptotic stability of positive equilibria is established under conditions slightly stronger than the ones required for the linear stability. For the case of monotone interactions, however, sharper conditions are presented. This paper generalizes known results for discrete delays to systems with distributed delays. Several applications illustrate the results.
publishDate 2008
dc.date.none.fl_str_mv 2008-03-01
2008-03-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://hdl.handle.net/1822/8041
url https://hdl.handle.net/1822/8041
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv "Journal of Differential Equations". ISSN 0022-0396. 244:5 (Mar. 2008) 1049-1079.
0022-0396
10.1016/j.jde.2007.12.005
http://www.sciencedirect.com/science/journal/00220396
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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