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Synchronization in model networks of class I neurons

Katriel, Guy (2003) Synchronization in model networks of class I neurons. [Preprint]

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Abstract

We study a modification of the Hoppensteadt-Izhikevich canonical model for networks of class I neurons, in which the 'pulse' emitted by a neuron is smooth rather than a delta-function. We prove two types of results about synchronization and desynchronization of such networks, the first type pertaining to 'pulse' functions which are symmetric, and the other type in the regime in which each neuron is connected to many other neurons.

Item Type:Preprint
Additional Information:An error in the asymptotic analysis in section 5 of the first version of the paper is corrected.
Subjects:Neuroscience > Neural Modelling
Neuroscience > Computational Neuroscience
Computer Science > Neural Nets
ID Code:3181
Deposited By:Katriel, Dr Guy
Deposited On:06 Oct 2003
Last Modified:12 Sep 2007 17:48

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References in Article

Select the SEEK icon to attempt to find the referenced article. If it does not appear to be in cogprints you will be forwarded to the paracite service. Poorly formated references will probably not work.

G.B. Ermentrout, Type I membranes, phase resetting curves and synchrony, Neural Comput. 8 (1996), 979-1001.

D. Hansel, G. Mato and C. Meunier, Synchrony in excitatory neural networks, Neural Comput. 7 (1995), 307-335.

F.C. Hoppensteadt & E.M. Izhikevich, `Weakly Connected Neural Networks', Springer-Verlag (New-York), 1997.

E.M. Izhikevich, Class 1 neural excitability, conventional synapses, weakly connected networks, and mathematical

foundations of pulse-coupled models, IEEE Trans. Neural Networks 10 (1999), 499-507.

G. Katriel, Stability of synchronized oscillations in

networks of phase-oscillators, preprint,

http://arxiv.org/abs/nlin.PS/0308031 .

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