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

top
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

top

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

top
  1. 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.  
  2. G.A. Chauvet. The use of representation and formalism in a theoretical approach to integrative neuroscience. J. Integr. Neurosci., 4 (2005), 291–312.  
  3. 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.  
  4. 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
  5. F. C. Hoppensteadt, E. Izhikevich. Weakly connected neural networks. Springer-Verlag, New York, 1997.  Zbl0887.92003
  6. E. M. Izhikevich. Dynamical Systems in Neuroscience: The geometry of excitability and bursting. The MIT Press, 2007.  
  7. E. M. Izhikevich. Phase equations for relaxation oscillators. SIAM J. Appl. Math., 60 (2000), 1789-1804.  Zbl1016.92001
  8. E.M. Izhikevich. Which model to use for cortical spiking neurons?. IEEE Trans Neural Netw, 15 (2004), 1063–1070.  
  9. 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
  10. 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
  11. C. Meunier, I. Segev. Playing the devil’s advocate: is the Hodgkin-Huxley model useful?. Trends Neurosci., 25 (2002), 558–563.  
  12. J. Modolo. Modélisation et analyse mathématique des effets de la stimulation cérébrale profonde dans la maladie de Parkinson. Thêse 2008.  
  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. 
  15. J. Modolo, E. Mosekilde, A. Beuter, New insights offered by a computational model of deep brain stimulation. J. Physiol. Paris, 101 (2007), 56–63.  
  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. 

NotesEmbed ?

top

You must be logged in to post comments.

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

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.