Population density models of integrate-and- fire neurons with jumps: Well-posedness
HENRY, Jacques
Institut de Mathématiques de Bordeaux [IMB]
SIgnals and SYstems in PHysiology & Engineering [SISYPHE]
Institut de Mathématiques de Bordeaux [IMB]
SIgnals and SYstems in PHysiology & Engineering [SISYPHE]
HENRY, Jacques
Institut de Mathématiques de Bordeaux [IMB]
SIgnals and SYstems in PHysiology & Engineering [SISYPHE]
< Leer menos
Institut de Mathématiques de Bordeaux [IMB]
SIgnals and SYstems in PHysiology & Engineering [SISYPHE]
Idioma
en
Article de revue
Este ítem está publicado en
Journal of Mathematical Biology. 2012-06-20
Springer
Resumen en inglés
In this paper we study the well-posedness of different models of population of leaky integrate- and- re neurons with a population density approach. The synaptic interaction between neurons is modeled by a potential jump ...Leer más >
In this paper we study the well-posedness of different models of population of leaky integrate- and- re neurons with a population density approach. The synaptic interaction between neurons is modeled by a potential jump at the reception of a spike. We study populations that are self excitatory or self inhibitory. We distinguish the cases where this interaction is instantaneous from the one where there is a repartition of conduction delays. In the case of a bounded density of delays both excitatory and inhibitory population models are shown to be well-posed. But without conduction delay the solution of the model of self excitatory neurons may blow up. We analyze the di erent behaviours of the model with jumps compared to its di usion approximation.< Leer menos
Palabras clave en inglés
Population density approach
Neural network
Coupled population
Integrate-and-fire
Nonlocal nonlinear partial differential equation
Well-posedness
Orígen
Importado de HalCentros de investigación