# 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

## Access Full Article

top## Abstract

top## How to cite

topGarenne, 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

top- O. Bennani, G. Chauvet, P. Chauvet, J.M. Dupont, F. Jouen. A hierarchical modeling approach of hippocampus local circuit. J. Integr. Neurosci.,9 (2009), 49–76.
- G.A. Chauvet. The use of representation and formalism in a theoretical approach to integrative neuroscience. J. Integr. Neurosci., 4 (2005), 291–312.
- C. Dejean, C.E. Gross, B. Bioulac, T. Boraud. Dynamic changes in the cortex-basal ganglia network after dopamine depletion in the rat. J. Neurophysiol., 100 (2008), 385–396.
- O. Faugeras, F. Grimbert J.-J. Slotine. Absolute stability and complete synchronization in a class of neural fields models. SIAM J. Appl. Math., 61 (2008), No. 1, 205-250. Zbl1227.34074
- F. C. Hoppensteadt, E. Izhikevich. Weakly connected neural networks. Springer-Verlag, New York, 1997. Zbl0887.92003
- E. M. Izhikevich. Dynamical Systems in Neuroscience: The geometry of excitability and bursting. The MIT Press, 2007.
- E. M. Izhikevich. Phase equations for relaxation oscillators. SIAM J. Appl. Math., 60 (2000), 1789-1804. Zbl1016.92001
- E.M. Izhikevich. Which model to use for cortical spiking neurons?. IEEE Trans Neural Netw, 15 (2004), 1063–1070.
- N. Koppel, G.B. Ermentrout. Mechanisms of phase-locking and frequency control in pairs of coupled neural oscillators. Handbook of Dynamical Systems, 2 (2002), 3–54. Zbl1105.92320
- G. S. Medvedev, N. Koppel. Synchronization and transient dynamics in the chains of electrically coupled Fitzhugh-Nagumo oscillators. SIAM J. Appl. Math., 60 (2001), No. 5, 1762–1801. Zbl0984.34027
- C. Meunier, I. Segev. Playing the devil’s advocate: is the Hodgkin-Huxley model useful?. Trends Neurosci., 25 (2002), 558–563.
- J. Modolo. Modélisation et analyse mathématique des effets de la stimulation cérébrale profonde dans la maladie de Parkinson. Thêse 2008.
- 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.
- 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.
- J. Modolo, E. Mosekilde, A. Beuter, New insights offered by a computational model of deep brain stimulation. J. Physiol. Paris, 101 (2007), 56–63.
- D. Serre. Systemes de lois the conservation I. Hyperbolicité, entropies, ondes de choc. Diederot Editeur, Paris, 1996.
- J.H. Sheeba, A. Stefanovska, P.V. McClintock. Neuronal synchrony during anesthesia: a thalamocortical model. Biophys. J., 95 (2008), 2722–2727.

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.