Email updates

Keep up to date with the latest news and content from BMC Neuroscience and BioMed Central.

This article is part of the supplement: Sixteenth Annual Computational Neuroscience Meeting: CNS*2007

Open Access Poster presentation

Revisiting time discretisation of spiking network models

Bruno Cessac2 and Thierry Viéville1*

  • * Corresponding author: Thierry Viéville

Author Affiliations

1 Odyssee Lab, INRIA, Sophia, France

2 INLN, Univ. of Nice-Sophia-Antipolis, France

For all author emails, please log on.

BMC Neuroscience 2007, 8(Suppl 2):P76  doi:10.1186/1471-2202-8-S2-P76


The electronic version of this article is the complete one and can be found online at:


Published:6 July 2007

© 2007 Cessac and Viéville; licensee BioMed Central Ltd.

Poster presentation

A link is built between a biologically plausible generalized integrate and fire (GIF) neuron model with conductance-based dynamics [1] and a discrete time neural network model with spiking neurons [2], for which rigorous results on the spontaneous dynamics has been obtained. More precisely the following has been shown.

i) Occurrence of periodic orbits is the generic regime of activity, with a bounded period in the presence of spike-time dependence plasticity, and arbitrary large periods at the edge of chaos (such regime is indistinguishable from chaos in numerical experiments, explaining what is obtained in [2]),

ii) the dynamics of membrane potential has a one to one correspondence with sequences of spikes patterns ("raster plots").

This allows a better insight into the possible neural coding in such a network and provides a deep understanding, at the network level, of the system behavior. Moreover, though the dynamics is generically periodic, it has a weak form of initial conditions sensitivity due to the presence of the sharp spiking threshold [3]. A step further, constructive conditions are derived, allowing to properly implement visual functions on such networks [4].

The time discretisation has been carefully conducted avoiding usual bias induced by e.g. Euler methods and taking into account a rather complex GIF model for which the usual arbitrary discontinuities are discussed in detail. The effects of the discretisation approximation have been analytically and experimentally analyzed, in detail.

thumbnailFigure 1. A view of the numerical experiments software platform raster-plot output, considering either a generic fully connected network or, here, a retinotopic network related to visual functions (top-left: 2D instantaneous spiking activity).

Acknowledgements

This work was partially supported by the EC IP project FP6-015879, FACETS.

References

  1. Rudolph M, Destexhe A: Analytical integrate and fire neuron models with conductance-based dynamics for event driven simulation strategies.

    Neural Computation 2006, 18:2146-2210. PubMed Abstract | Publisher Full Text OpenURL

  2. Soula H, Beslon G, Mazet O: Spontaneous dynamics of asymmetric random recurrent spiking neural networks.

    Neural Computation 2006., 18(1) PubMed Abstract | Publisher Full Text OpenURL

  3. Cessac B: A discrete time neural network model with spiking neurons. i. rigorous results on the spontaneous dynamics.

    [A PRECISER], in press. OpenURL

  4. Viéville T, Kornprobst P: Modeling cortical maps with feed-backs.

    Int Joint Conf on Neural Networks 2006. OpenURL