Geodesic
Analysis of Synchronization in a Neural Population by a Population Density Approach
A. Garenne1, 2 ; J. Henry3 ; C. O. Tarniceriu3, 4
1 Basal Gang, Laboratoire Mouvement, Adaptation, Cognition, CNRS-UMR 5227, Bordeaux, France
2 Université Victor Segalen Bordeaux 2, Bordeaux, France
3 INRIA Bordeaux Sud Ouest IMB, 351, Cours de la Libération, 33405 Talence cedex, France
4 Department of Sciences, "Al. I. Cuza University", Iaşi, Romania
Mathematical modelling of natural phenomena, Tome 5 (2010) no. 2, pp. 5-25.

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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.
DOI : 10.1051/mmnp/20105201

A. Garenne 1, 2 ; J. Henry 3 ; C. O. Tarniceriu 3, 4

1 Basal Gang, Laboratoire Mouvement, Adaptation, Cognition, CNRS-UMR 5227, Bordeaux, France
2 Université Victor Segalen Bordeaux 2, Bordeaux, France
3 INRIA Bordeaux Sud Ouest IMB, 351, Cours de la Libération, 33405 Talence cedex, France
4 Department of Sciences, "Al. I. Cuza University", Iaşi, Romania 
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A. Garenne; J. Henry; C. O. Tarniceriu. Analysis of Synchronization in a Neural Population by a Population Density Approach. Mathematical modelling of natural phenomena, Tome 5 (2010) no. 2, pp. 5-25. doi : 10.1051/mmnp/20105201. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20105201/

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