{"id":92780,"date":"2018-03-11T10:11:53","date_gmt":"2018-03-11T10:11:53","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/synchronization-and-chaos-in-coupled-systems-the-model-of-two-coupled-brusselators\/"},"modified":"2018-03-11T10:11:53","modified_gmt":"2018-03-11T10:11:53","slug":"synchronization-and-chaos-in-coupled-systems-the-model-of-two-coupled-brusselators","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/biomatematicas\/synchronization-and-chaos-in-coupled-systems-the-model-of-two-coupled-brusselators\/","title":{"rendered":"Synchronization and chaos in coupled systems: the model of two coupled brusselators"},"content":{"rendered":"<h2>Tesis doctoral de <strong> F\u00e1tima Drubi Vega <\/strong><\/h2>\n<p>Esta tesis aborda problemas relativos al estudio de sistemas acoplados. Se trata de modelos que surgen en todos los campos de la ciencia y generan un abanico de cuestiones extremadamente amplio. nuestro inter\u00e9s se focaliza en la b\u00fasqueda de la respuesta a una pregunta muy concreta: \u00c2\u00bfcabe la posibilidad de generar din\u00e1mica ca\u00f3tica mediante el acoplamiento simple de din\u00e1micas simples?  en el mundo de los sistemas din\u00e1micos son bien conocidas las dificultades que encierran las pruebas anal\u00edticas de existencia de comportamientos ca\u00f3ticos. Aunque son conocidas configuraciones globales cuya presencia implica, bajo condiciones gen\u00e9ricas, la g\u00e9nesis de din\u00e1mica ca\u00f3tica, \u00e9stas son dif\u00edciles de detectar en situaciones espec\u00edficas. Afortunadamente, disponemos de resultados que afirman la aparici\u00f3n de las configuraciones apropiadas, de nuevo bajo condiciones gen\u00e9ricas, en el entorno de ciertas singularidades. Obs\u00e9rvese que las singularidades son objetos m\u00e1s f\u00e1cilmente detectables.  nuestro principal logro es el haber dado una respuesta positiva a la pregunta formulada anteriormente. Para ello ha sido necesario un desarrollo te\u00f3rico que nos ha permitido probar en un modelo espec\u00edfico la existencia de singularidades que explican la g\u00e9nesis de din\u00e1mica ca\u00f3tica. Estos resultados est\u00e1n recogidos en las siguientes publicaciones:  &#8211; f. Drubi, s. Ib\u00e1\u00f1ez y j. A. Rodr\u00edguez, coupling leads to chaos, journal of differential equations, 239, 371-385, (2007),  &#8211; f. Drubi, s. Ib\u00e1\u00f1ez y j. A. Rodr\u00edguez, singularities and chaos in coupled systems, bulletin of the belgian mathematical society, 15, 797-808, (2008).  las singularidades que se tratan en estos trabajos son conocidas como singularidades nilpotentes.  en esta tesis se incluye adem\u00e1s un estudio exhaustivo del mapa de singularidades que surgen en el modelo bajo an\u00e1lisis. De entre ellas, como aportaci\u00f3n adicional se estudian con mayor profundidad las singularidades hopf-pitchfork, contribuyendo al conocimiento general de sus bifurcaciones. De los diferentes tipos que aparecen unas nos permiten entender los fen\u00f3menos de sincronizaci\u00f3n, de tanta relevancia en sistemas acoplados, y otras se convierten, nuevamente, en posibles centros organizadores de din\u00e1mica ca\u00f3tica. Un primer trabajo ha sido sometido a los proceedins equadiff 2007:  &#8211; f. Drubi, s. Ib\u00e1\u00f1ez, j. A. Rodriguez, chaotic dynamics in coupled systems.  adem\u00e1s, una publicaci\u00f3n recogiendo todos estos nuevos resultados se encuentra actualmente en proceso de elaboraci\u00f3n.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Synchronization and chaos in coupled systems: the model of two coupled brusselators<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Synchronization and chaos in coupled systems: the model of two coupled brusselators <\/li>\n<li><strong>Autor:<\/strong>\u00a0 F\u00e1tima Drubi Vega <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Oviedo<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 15\/04\/2009<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Santiago F. Ib\u00e1\u00f1ez Mesa<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: martin Golubitsky <\/li>\n<li>freddy Dumortier (vocal)<\/li>\n<li>armengol Gasull embid (vocal)<\/li>\n<li>Emilio Freire mac\u00edas (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de F\u00e1tima Drubi Vega Esta tesis aborda problemas relativos al estudio de sistemas acoplados. Se trata de modelos [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[7016,12585,8846],"tags":[29387,50970,191802,25415,191804,191803],"class_list":["post-92780","post","type-post","status-publish","format-standard","hentry","category-biomatematicas","category-ecuaciones-diferenciales-ordinarias","category-oviedo","tag-armengol-gasull-embid","tag-emilio-freire-macias","tag-fatima-drubi-vega","tag-freddy-dumortier","tag-martin-golubitsky","tag-santiago-f-ibanez-mesa"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/92780","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/comments?post=92780"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/92780\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=92780"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=92780"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=92780"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}