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

Published online by Cambridge University Press:  10 March 2010

A. Garenne ,
J. Henry  and
C. O. Tarniceriu
A. Garenne
Affiliation:
Basal Gang, Laboratoire Mouvement, Adaptation, Cognition, CNRS-UMR 5227, Bordeaux, France Université Victor Segalen Bordeaux 2, Bordeaux, France
J. Henry*
Affiliation:
INRIA Bordeaux Sud Ouest IMB, 351, Cours de la Libération, 33405 Talence cedex, France
C. O. Tarniceriu
Affiliation:
INRIA Bordeaux Sud Ouest IMB, 351, Cours de la Libération, 33405 Talence cedex, France Department of Sciences, "Al. I. Cuza University", Iaşi, Romania
*
* Corresponding author. E-mail: Jacques.Henry@math.u-bordeaux1.fr
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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.

Keywords

single neuron modelpopulation density approachsynchronization
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 2: Mathematics and neuroscience , 2010 , pp. 5 - 25
Copyright
© EDP Sciences, 2010

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