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

André Garenne; Jacques Henry; Carmen Oana Tarniceriu

HAL: inria-00482420, version 1

DOI: 10.1051/mmnp/20105201

See short view

BibTeX,EndNote,...

Analysis of Synchronization in a Neural Population by a Population Density Approach
Garenne A., Henry J., Tarniceriu C. O.
Mathematical Modelling of Natural Phenomena 5, 2 (2010) 5-25 - http://hal.inria.fr/inria-00482420

Type of document:

Articles in peer-reviewed journal

Domain:

Mathematics/Analysis of PDEs

Life Sciences/Neurons and Cognition/Neurobiology

Title:

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

Author(s):

André Garenne ¹, Jacques Henry (

) ^2, 3, Carmen Oana Tarniceriu (

) ³

Research team(s):

1:	Laboratoire Mouvement Adaptation Cognition (MAC)

	Université Victor Segalen - Bordeaux II – CNRS : UMR5227

	Zone nord Bat 2, 2e étage, 146, rue Léo Saignat, 33076 Bordeaux Cedex, France

	France

2:	Institut de Mathématiques de Bordeaux (IMB)

	http://www.math.u-bordeaux.fr/IMB/

	CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II

	351 cours de la Libération 33405 TALENCE CEDEX

	France

3:	ANUBIS (INRIA Bordeaux - Sud-Ouest)

	INRIA – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II – CNRS : UMR

	France

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.

Full text language:

English

Journal title:

Mathematical Modelling of Natural Phenomena

Publication date:

2010-03

Audience:

international

Commercial editor:

EDP science

Volume title :

Mathematics and neurosciences

Volume:

Number:

Pagination:

5-25

Keywords:

Single neuron model – Population density approach – Synchronization

Contract, financing:

programme CNRS neuroinformatique

Attached file list to this document:

PDF

synchr-f5.pdf

(225.4 KB)


inria-00482420, version 1
http://hal.inria.fr/inria-00482420
oai:hal.inria.fr:inria-00482420
From: Jacques Henry <>
Submitted on: Monday, 10 May 2010 14:29:15
Updated on: Sunday, 16 May 2010 11:15:34