| Issue |
Math. Model. Nat. Phenom.
Volume 5, Number 2, 2010
Mathematics and neuroscience
|
|
|---|---|---|
| Page(s) | 5 - 25 | |
| DOI | https://doi.org/10.1051/mmnp/20105201 | |
| Published online | 10 March 2010 | |
Analysis of Synchronization in a Neural Population by a Population Density Approach
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
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
© EDP Sciences, 2010
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