Math. Model. Nat. Phenom.
Volume 5, Number 2, 2010Mathematics and neuroscience
|Page(s)||5 - 25|
|Published online||10 March 2010|
Analysis of Synchronization in a Neural Population by a Population Density Approach
INRIA Bordeaux Sud Ouest IMB, 351, Cours de la Libération, 33405
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:
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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