DUMONT, Grégory; HENRY, Jacques

doi:10.1007/s11538-013-9823-8

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DUMONT, Grégory
Institut de Mathématiques de Bordeaux [IMB]
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]

HENRY, Jacques
Institut de Mathématiques de Bordeaux [IMB]
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]

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Bulletin of Mathematical Biology. 2013-02-22, vol. 75, n° 4, p. 629-648

Springer Verlag

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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.< Réduire

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Population of neurons

Partial differential equation

Blow up

Synchronization

Integrate-and-fire

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Synchronization of an Excitatory Integrate-and-Fire Neural Network

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