Critical behavior of the delay-induced chaos transition in a nonlinear model for the immune response

Detalhes bibliográficos
Autor(a) principal: Souza,Elder de
Data de Publicação: 2009
Outros Autores: Lyra,Marcelo, Gleria,Iram
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Brazilian Journal of Physics
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332009000400015
Resumo: In this paper we analyze a model for the dynamics of the immune system interacting with a target population. The model consists in a set of two-dimensional delayed differential equations. The model is effectively infinite dimensional due to the presence of the delay and chaotic regimes can be supported. We show that a delayed response induces sustained oscillations and larger delay times implies in a series of bifurcations leading to chaos. The characteristic exponent of the critical power law relaxation towards the stationary state is obtained as well as the critical exponent governing the vanishing of the order parameter in the vicinity of the chaotic transition.
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spelling Critical behavior of the delay-induced chaos transition in a nonlinear model for the immune responseDelayed systemsImmune responseChaosIn this paper we analyze a model for the dynamics of the immune system interacting with a target population. The model consists in a set of two-dimensional delayed differential equations. The model is effectively infinite dimensional due to the presence of the delay and chaotic regimes can be supported. We show that a delayed response induces sustained oscillations and larger delay times implies in a series of bifurcations leading to chaos. The characteristic exponent of the critical power law relaxation towards the stationary state is obtained as well as the critical exponent governing the vanishing of the order parameter in the vicinity of the chaotic transition.Sociedade Brasileira de Física2009-08-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332009000400015Brazilian Journal of Physics v.39 n.2a 2009reponame:Brazilian Journal of Physicsinstname:Sociedade Brasileira de Física (SBF)instacron:SBF10.1590/S0103-97332009000400015info:eu-repo/semantics/openAccessSouza,Elder deLyra,MarceloGleria,Irameng2009-09-10T00:00:00Zoai:scielo:S0103-97332009000400015Revistahttp://www.sbfisica.org.br/v1/home/index.php/pt/ONGhttps://old.scielo.br/oai/scielo-oai.phpsbfisica@sbfisica.org.br||sbfisica@sbfisica.org.br1678-44480103-9733opendoar:2009-09-10T00:00Brazilian Journal of Physics - Sociedade Brasileira de Física (SBF)false
dc.title.none.fl_str_mv Critical behavior of the delay-induced chaos transition in a nonlinear model for the immune response
title Critical behavior of the delay-induced chaos transition in a nonlinear model for the immune response
spellingShingle Critical behavior of the delay-induced chaos transition in a nonlinear model for the immune response
Souza,Elder de
Delayed systems
Immune response
Chaos
title_short Critical behavior of the delay-induced chaos transition in a nonlinear model for the immune response
title_full Critical behavior of the delay-induced chaos transition in a nonlinear model for the immune response
title_fullStr Critical behavior of the delay-induced chaos transition in a nonlinear model for the immune response
title_full_unstemmed Critical behavior of the delay-induced chaos transition in a nonlinear model for the immune response
title_sort Critical behavior of the delay-induced chaos transition in a nonlinear model for the immune response
author Souza,Elder de
author_facet Souza,Elder de
Lyra,Marcelo
Gleria,Iram
author_role author
author2 Lyra,Marcelo
Gleria,Iram
author2_role author
author
dc.contributor.author.fl_str_mv Souza,Elder de
Lyra,Marcelo
Gleria,Iram
dc.subject.por.fl_str_mv Delayed systems
Immune response
Chaos
topic Delayed systems
Immune response
Chaos
description In this paper we analyze a model for the dynamics of the immune system interacting with a target population. The model consists in a set of two-dimensional delayed differential equations. The model is effectively infinite dimensional due to the presence of the delay and chaotic regimes can be supported. We show that a delayed response induces sustained oscillations and larger delay times implies in a series of bifurcations leading to chaos. The characteristic exponent of the critical power law relaxation towards the stationary state is obtained as well as the critical exponent governing the vanishing of the order parameter in the vicinity of the chaotic transition.
publishDate 2009
dc.date.none.fl_str_mv 2009-08-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332009000400015
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0103-97332009000400015
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S0103-97332009000400015
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Física
publisher.none.fl_str_mv Sociedade Brasileira de Física
dc.source.none.fl_str_mv Brazilian Journal of Physics v.39 n.2a 2009
reponame:Brazilian Journal of Physics
instname:Sociedade Brasileira de Física (SBF)
instacron:SBF
instname_str Sociedade Brasileira de Física (SBF)
instacron_str SBF
institution SBF
reponame_str Brazilian Journal of Physics
collection Brazilian Journal of Physics
repository.name.fl_str_mv Brazilian Journal of Physics - Sociedade Brasileira de Física (SBF)
repository.mail.fl_str_mv sbfisica@sbfisica.org.br||sbfisica@sbfisica.org.br
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