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

Issue		Math. Model. Nat. Phenom. Volume 5, Number 2, 2010 Mathematics and neuroscience


Page(s)		5 - 25
DOI		10.1051/mmnp/20105201
Published online		10 March 2010

Math. Model. Nat. Phenom. Vol. 5, No. 2, 2010, pp. 5-25

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

A. Garenne²^,3, J. Henry¹^* and C. O. Tarniceriu¹^,4

¹ INRIA Bordeaux Sud Ouest IMB, 351, Cours de la Libération, 33405 Talence cedex, France
² Basal Gang, Laboratoire Mouvement, Adaptation, Cognition, CNRS-UMR 5227, Bordeaux, France
³ Université Victor Segalen Bordeaux 2, Bordeaux, France
⁴ Department of Sciences, ”Al. I. Cuza University”, Iaşi, Romania

^* Corresponding author. E-mail: Jacques.Henry@math.u-bordeaux1.fr

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.

Mathematics Subject Classification: 92C20 / 92D25 / 34D10 / 35L65

Key words: single neuron model / population density approach / synchronization

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