Dynamics of a neuronal model, Synchronizaton and Complexity
Identifieur interne : 000104 ( Hal/Curation ); précédent : 000103; suivant : 000105Dynamics of a neuronal model, Synchronizaton and Complexity
Auteurs : Nathalie Corson [France]Source :
Descripteurs français
- mix :
English descriptors
- mix :
Abstract
The neuron is a point of interest in various scientific domains as a fundamental cell in the nervous system. Some mathematical models describing neuron behaviour exist. When some of these models interact due to coupling functions, the network behaviour can be analyzed as a complex system, . Firstly, this work presents the main mechanisms governing the neuron behaviour in order to understand the different models. Several models are then presented, including the Hindmarsh-Rose one, dating from 1984. The numerical and theoretical study of the asymptotic and transitory dynamics of the forementioned model is then proposed in the second part of this thesis. In the third part, interaction networks are constructed coupling many of these models. These networks are first studied in terms of complete synchronization. Consequently, some properties emerge, some of which are characterized by power laws. Finally, an algorithm of burst synchronization detection is developped.
Url:
Links toward previous steps (curation, corpus...)
- to stream Hal, to step Corpus: Pour aller vers cette notice dans l'étape Curation :000104
Links to Exploration step
Hal:tel-00453912Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Dynamics of a neuronal model, Synchronizaton and Complexity</title><title xml:lang="fr">Dynamique d'un modèle neuronal, synchronisation et complexité</title><author><name sortKey="Corson, Nathalie" sort="Corson, Nathalie" uniqKey="Corson N" first="Nathalie" last="Corson">Nathalie Corson</name><affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-87" status="VALID"><orgName>Laboratoire de Mathématiques Appliquées du Havre</orgName><orgName type="acronym">LMAH</orgName><desc><address><country key="FR"></country></address><ref type="url">http://www-lmah.univ-lehavre.fr</ref></desc><listRelation><relation active="#struct-300317" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-300317" type="direct"><org type="institution" xml:id="struct-300317" status="VALID"><orgName>Université du Havre</orgName><desc><address><country key="FR"></country></address></desc></org></tutelle></tutelles></hal:affiliation><country>France</country><placeName><settlement type="city">Le Havre</settlement><region type="region" nuts="2">Région Normandie</region><region type="old region" nuts="2">Haute-Normandie</region></placeName><orgName type="university">Université du Havre</orgName></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">HAL</idno><idno type="RBID">Hal:tel-00453912</idno><idno type="halId">tel-00453912</idno><idno type="halUri">https://tel.archives-ouvertes.fr/tel-00453912</idno><idno type="url">https://tel.archives-ouvertes.fr/tel-00453912</idno><date when="2009-12-02">2009-12-02</date><idno type="wicri:Area/Hal/Corpus">000104</idno><idno type="wicri:Area/Hal/Curation">000104</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Dynamics of a neuronal model, Synchronizaton and Complexity</title><title xml:lang="fr">Dynamique d'un modèle neuronal, synchronisation et complexité</title><author><name sortKey="Corson, Nathalie" sort="Corson, Nathalie" uniqKey="Corson N" first="Nathalie" last="Corson">Nathalie Corson</name><affiliation wicri:level="1"><hal:affiliation type="laboratory" xml:id="struct-87" status="VALID"><orgName>Laboratoire de Mathématiques Appliquées du Havre</orgName><orgName type="acronym">LMAH</orgName><desc><address><country key="FR"></country></address><ref type="url">http://www-lmah.univ-lehavre.fr</ref></desc><listRelation><relation active="#struct-300317" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-300317" type="direct"><org type="institution" xml:id="struct-300317" status="VALID"><orgName>Université du Havre</orgName><desc><address><country key="FR"></country></address></desc></org></tutelle></tutelles></hal:affiliation><country>France</country><placeName><settlement type="city">Le Havre</settlement><region type="region" nuts="2">Région Normandie</region><region type="old region" nuts="2">Haute-Normandie</region></placeName><orgName type="university">Université du Havre</orgName></affiliation></author></analytic></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term>complex systems</term><term>differential equations</term><term>modeling</term><term>nonlinear dynamical systems</term><term>synchronization</term></keywords><keywords scheme="mix" xml:lang="fr"><term>applications</term><term>bifurcations</term><term>modélisation</term><term>synchronisation</term><term>systèmes complexes</term><term>systèmes dynamiques non-linéaires</term><term>équations différentielles</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">The neuron is a point of interest in various scientific domains as a fundamental cell in the nervous system. Some mathematical models describing neuron behaviour exist. When some of these models interact due to coupling functions, the network behaviour can be analyzed as a complex system, . Firstly, this work presents the main mechanisms governing the neuron behaviour in order to understand the different models. Several models are then presented, including the Hindmarsh-Rose one, dating from 1984. The numerical and theoretical study of the asymptotic and transitory dynamics of the forementioned model is then proposed in the second part of this thesis. In the third part, interaction networks are constructed coupling many of these models. These networks are first studied in terms of complete synchronization. Consequently, some properties emerge, some of which are characterized by power laws. Finally, an algorithm of burst synchronization detection is developped.</div></front></TEI><hal api="V3"><titleStmt><title xml:lang="en">Dynamics of a neuronal model, Synchronizaton and Complexity</title><title xml:lang="fr">Dynamique d'un modèle neuronal, synchronisation et complexité</title><author role="aut"><persName><forename type="first">Nathalie</forename><surname>Corson</surname></persName><email>nathalie.corson@gmail.com</email><idno type="halauthor">445780</idno><affiliation ref="#struct-87"></affiliation></author><editor role="depositor"><persName><forename>Nathalie</forename><surname>Corson</surname></persName><email>nathalie.corson@gmail.com</email></editor></titleStmt><editionStmt><edition n="v1"><date type="whenSubmitted">2010-02-05 21:28:09</date></edition><edition n="v2" type="current"><date type="whenSubmitted">2010-02-19 11:24:44</date><date type="whenModified">2010-02-19 15:29:43</date><date type="whenReleased">2010-02-19 15:29:43</date><date type="whenProduced">2009-12-02</date><date type="whenEndEmbargoed">2010-02-19</date><ref type="file" target="https://tel.archives-ouvertes.fr/tel-00453912v2/document"><date notBefore="2010-02-19"></date></ref><ref type="file" n="1" target="https://tel.archives-ouvertes.fr/tel-00453912/file/these_NC.pdf"><date notBefore="2010-02-19"></date></ref></edition><respStmt><resp>contributor</resp><name key="138431"><persName><forename>Nathalie</forename><surname>Corson</surname></persName><email>nathalie.corson@gmail.com</email></name></respStmt></editionStmt><publicationStmt><distributor>CCSD</distributor><idno type="halId">tel-00453912</idno><idno type="halUri">https://tel.archives-ouvertes.fr/tel-00453912</idno><idno type="halBibtex">corson:tel-00453912</idno><idno type="halRefHtml">Mathématiques [math]. Université du Havre, 2009. Français</idno><idno type="halRef">Mathématiques [math]. Université du Havre, 2009. Français</idno></publicationStmt><seriesStmt><idno type="stamp" n="UNIV-LEHAVRE">Université du Havre</idno><idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno></seriesStmt><notesStmt></notesStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Dynamics of a neuronal model, Synchronizaton and Complexity</title><title xml:lang="fr">Dynamique d'un modèle neuronal, synchronisation et complexité</title><author role="aut"><persName><forename type="first">Nathalie</forename><surname>Corson</surname></persName><email>nathalie.corson@gmail.com</email><idno type="halAuthorId">445780</idno><affiliation ref="#struct-87"></affiliation></author></analytic><monogr><imprint><date type="dateDefended">2009-12-02</date></imprint><authority type="institution">Université du Havre</authority><authority type="supervisor">M.A. Aziz-Alaoui</authority><authority type="jury">Pierre Collet (Président du jury)</authority><authority type="jury">Guanrong (Ron) Chen (rapporteur)</authority><authority type="jury">René Lozi (rapporteur)</authority><authority type="jury">Cyrille Bertelle (examinateur)</authority><authority type="jury">Jean-Pierre Françoise (examinateur)</authority><authority type="jury">Adnan Yassine (examinateur)</authority><authority type="jury">M.A. Aziz-Alaoui (directeur)</authority></monogr></biblStruct></sourceDesc><profileDesc><langUsage><language ident="fr">French</language></langUsage><textClass><keywords scheme="author"><term xml:lang="en">nonlinear dynamical systems</term><term xml:lang="en">differential equations</term><term xml:lang="en">synchronization</term><term xml:lang="en">modeling</term><term xml:lang="en">complex systems</term><term xml:lang="fr">systèmes dynamiques non-linéaires</term><term xml:lang="fr">équations différentielles</term><term xml:lang="fr">bifurcations</term><term xml:lang="fr">synchronisation</term><term xml:lang="fr">modélisation</term><term xml:lang="fr">systèmes complexes</term><term xml:lang="fr">applications</term></keywords><classCode scheme="halDomain" n="math">Mathematics [math]</classCode><classCode scheme="halTypology" n="THESE">Theses</classCode></textClass><abstract xml:lang="en">The neuron is a point of interest in various scientific domains as a fundamental cell in the nervous system. Some mathematical models describing neuron behaviour exist. When some of these models interact due to coupling functions, the network behaviour can be analyzed as a complex system, . Firstly, this work presents the main mechanisms governing the neuron behaviour in order to understand the different models. Several models are then presented, including the Hindmarsh-Rose one, dating from 1984. The numerical and theoretical study of the asymptotic and transitory dynamics of the forementioned model is then proposed in the second part of this thesis. In the third part, interaction networks are constructed coupling many of these models. These networks are first studied in terms of complete synchronization. Consequently, some properties emerge, some of which are characterized by power laws. Finally, an algorithm of burst synchronization detection is developped.</abstract><abstract xml:lang="fr">Le fonctionnement d'un neurone, cellule fondamentale du système nerveux, intéresse de nombreuses disciplines scientifiques. Il existe ainsi des modèles mathématiques qui décrivent leur comportement par des systèmes d'EDO. Plusieurs de ces modèles peuvent ensuite être couplés afin de pouvoir étudier le comportement de réseaux, systèmes complexes au sein desquels émergent des propriétés. Ce travail présente, dans un premier temps, les principaux mécanismes régissant ce fonctionnement afin d'en comprendre la modélisation. Plusieurs modèles sont alors présentés, jusqu'à celui de Hindmarsh-Rose (1984), qui présente une dynamique lente-rapide. C'est sur l'étude numérique mais également théorique de la dynamique asymptotique et transitoire de ce dernier modèle, que se concentre la seconde partie de cette thèse. Dans une troisième partie, des réseaux d'interactions sont construits en couplant les systèmes dynamiques précédemment étudiés. L'étude du phénomène de synchronisation complète au sein de ces réseaux montre l'existence de propriétés émergentes pouvant être caractérisées par des lois de puissance. Enfin, un algorithme de détection de la synchronisation de bursts est proposé.</abstract></profileDesc></hal></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/France/explor/LeHavreV1/Data/Hal/Curation
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000104 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Hal/Curation/biblio.hfd -nk 000104 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/France
|area= LeHavreV1
|flux= Hal
|étape= Curation
|type= RBID
|clé= Hal:tel-00453912
|texte= Dynamics of a neuronal model, Synchronizaton and Complexity
}}
| This area was generated with Dilib version V0.6.25. |  |