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

A. Garenne; J. Henry; C. O. Tarniceriu

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 2, page 5-25
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Garenne, A., Henry, J., and Tarniceriu, C. O.. "Analysis of Synchronization in a Neural Population by a Population Density Approach." Mathematical Modelling of Natural Phenomena 5.2 (2010): 5-25. <http://eudml.org/doc/197716>.

@article{Garenne2010,
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.},
author = {Garenne, A., Henry, J., Tarniceriu, C. O.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {single neuron model; population density approach; synchronization},
language = {eng},
month = {3},
number = {2},
pages = {5-25},
publisher = {EDP Sciences},
title = {Analysis of Synchronization in a Neural Population by a Population Density Approach},
url = {http://eudml.org/doc/197716},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Garenne, A.
AU - Henry, J.
AU - Tarniceriu, C. O.
TI - Analysis of Synchronization in a Neural Population by a Population Density Approach
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/3//
PB - EDP Sciences
VL - 5
IS - 2
SP - 5
EP - 25
AB - 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.
LA - eng
KW - single neuron model; population density approach; synchronization
UR - http://eudml.org/doc/197716
ER -

References

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  13. J. Modolo, A. Garenne, J. Henry, A. Beuter. Development and validation of a neural population model based on the dynamics of discontinuous membrane potential neuron model. J. Integr. Neurosci., 6 (2007), No. 4, 625–656.  
  14. J. Modolo, J. Henry A. Beuter. Dynamics of the subthalamo-pallidal complex in Parkinson’s Disease during deep brain stimulation. J. Biol. Phys., 34 (2008), 351–366. 
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  16. D. Serre. Systemes de lois the conservation I. Hyperbolicité, entropies, ondes de choc. Diederot Editeur, Paris, 1996.  
  17. J.H. Sheeba, A. Stefanovska, P.V. McClintock. Neuronal synchrony during anesthesia: a thalamocortical model. Biophys. J., 95 (2008), 2722–2727. 

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