Dynamics of a neuronal model, Synchronizaton and Complexity
Identifieur interne : 000A68 ( Main/Exploration ); précédent : 000A67; suivant : 000A69Dynamics 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:
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream Hal, to step Corpus: 000104
- to stream Hal, to step Curation: 000104
- to stream Hal, to step Checkpoint: 000480
- to stream Main, to step Merge: 000A76
- to stream Main, to step Curation: 000A68
Le 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><idno type="wicri:Area/Hal/Checkpoint">000480</idno><idno type="wicri:Area/Main/Merge">000A76</idno><idno type="wicri:Area/Main/Curation">000A68</idno><idno type="wicri:Area/Main/Exploration">000A68</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><affiliations><list><country><li>France</li></country><region><li>Haute-Normandie</li><li>Région Normandie</li></region><settlement><li>Le Havre</li></settlement><orgName><li>Université du Havre</li></orgName></list><tree><country name="France"><region name="Région Normandie"><name sortKey="Corson, Nathalie" sort="Corson, Nathalie" uniqKey="Corson N" first="Nathalie" last="Corson">Nathalie Corson</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/France/explor/LeHavreV1/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000A68 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 000A68 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/France
|area= LeHavreV1
|flux= Main
|étape= Exploration
|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. |  |