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inria-00482420, version 1

Analysis of Synchronization in a Neural Population by a Population Density Approach

André Garenne 1, Jacques Henry (Author to contact preferably) 2, 3, Carmen Oana Tarniceriu () a, 3

Mathematical Modelling of Natural Phenomena 5, 2 (2010) 5-25

Abstract: In this paper we deal with a model describing the evolution in time of the density of a neural population in a state space, where the state is given by Izhikevich's two - dimensional single neuron model. The main goal is to mathematically describe the occurrence of a significant phenomenon observed in neurons populations, the synchronization. To this end, we are making the transition to phase density population, and use Malkin theorem to calculate the phase deviations of a weakly coupled population model.

  • a –  university Al. I. Cuza, Iasi, Roumanie
  • 1:  Laboratoire Mouvement Adaptation Cognition (MAC)
  • Université Victor Segalen - Bordeaux II – CNRS : UMR5227
  • 2:  Institut de Mathématiques de Bordeaux (IMB)
  • CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II
  • 3:  ANUBIS (INRIA Bordeaux - Sud-Ouest)
  • INRIA – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II – CNRS : UMR
  • Domain : Mathematics/Analysis of PDEs
    Life Sciences/Neurons and Cognition/Neurobiology
  • Keywords : Single neuron model – Population density approach – Synchronization
 
  • inria-00482420, version 1
  • http://hal.inria.fr/inria-00482420
  • oai:hal.inria.fr:inria-00482420
  • From: Jacques Henry <>
  • Submitted on: Monday, 10 May 2010 14:29:15
  • Updated on: Sunday, 16 May 2010 11:15:34