Synchronization of an Excitatory Integrate-and-Fire Neural Network
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN] | |
| dc.contributor.author | DUMONT, Grégory | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN] | |
| dc.contributor.author | HENRY, Jacques | |
| dc.date.accessioned | 2024-04-04T02:22:07Z | |
| dc.date.available | 2024-04-04T02:22:07Z | |
| dc.date.issued | 2013-02-22 | |
| dc.identifier.issn | 0092-8240 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189627 | |
| dc.description.abstractEn | In this paper, we study the influence of the coupling strength on the synchronization behavior of a population of leaky integrate-and-fire neurons that is selfexcitatory with a population density approach. Each neuron of the population is assumed to be stochastically driven by an independent Poisson spike train and the synaptic interaction between neurons is modeled by a potential jump at the reception of an action potential. Neglecting the synaptic delay, we will establish that for a strong enough connectivity between neurons, the solution of the partial differential equation which describes the population density function must blow up in finite time. Furthermore, we will give a mathematical estimate on the average connection per neuron to ensure the occurrence of a burst. Interpreting the blow up of the solution as the presence of a Dirac mass in the firing rate of the population, we will relate the blow up of the solution to the occurrence of the synchronization of neurons. Fully stochastic simulations of a finite size network of leaky integrate-and-fire neurons are performed to illustrate our theoretical results. | |
| dc.language.iso | en | |
| dc.publisher | Springer Verlag | |
| dc.subject.en | Population of neurons | |
| dc.subject.en | Partial differential equation | |
| dc.subject.en | Blow up | |
| dc.subject.en | Synchronization | |
| dc.subject.en | Integrate-and-fire | |
| dc.title.en | Synchronization of an Excitatory Integrate-and-Fire Neural Network | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s11538-013-9823-8 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| bordeaux.journal | Bulletin of Mathematical Biology | |
| bordeaux.page | 629-648 | |
| bordeaux.volume | 75 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 4 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00822472 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00822472v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Bulletin%20of%20Mathematical%20Biology&rft.date=2013-02-22&rft.volume=75&rft.issue=4&rft.spage=629-648&rft.epage=629-648&rft.eissn=0092-8240&rft.issn=0092-8240&rft.au=DUMONT,%20Gr%C3%A9gory&HENRY,%20Jacques&rft.genre=article |
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