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Synchronization of an Excitatory Integrate-and-Fire Neural Network

Grégory Dumont 1, 2 Jacques Henry 1, 2 
2 CARMEN - Modélisation et calculs pour l'électrophysiologie cardiaque
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest, IHU-LIRYC
Abstract : 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.
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Submitted on : Tuesday, May 14, 2013 - 5:02:50 PM
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Grégory Dumont, Jacques Henry. Synchronization of an Excitatory Integrate-and-Fire Neural Network. Bulletin of Mathematical Biology, Springer Verlag, 2013, 75 (4), pp.629-648. ⟨10.1007/s11538-013-9823-8⟩. ⟨hal-00822472⟩

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