title: Synchronization of an excitatory integrate-and-fire neural network.
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 self-excitatory 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.
authors: CNRS-Institut de Mathématiques de Bordeaux, Université de Bordeaux, Bordeaux, France. gregory.dumont@inria.fr
authors: Grégory
authors: G
authors: Dumont
authors: Jacques
authors: J
authors: Henry
mesh_terms: D000200:Action Potentials / Q000502:physiology; D001921:Brain / Q000166:cytology / Q000502:physiology*; D003198:Computer Simulation; D008564:Membrane Potentials / Q000502:physiology; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D009474:Neurons / Q000502:physiology*; D013269:Stochastic Processes