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Revisiting time discretisation of spiking network models

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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.

Figure 1
figure1

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).

References

  1. 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. 10.1162/neco.2006.18.9.2146.

  2. 2.

    Soula H, Beslon G, Mazet O: Spontaneous dynamics of asymmetric random recurrent spiking neural networks. Neural Computation. 2006, 18 (1):

  3. 3.

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

  4. 4.

    Viéville T, Kornprobst P: Modeling cortical maps with feed-backs. Int Joint Conf on Neural Networks. 2006

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Acknowledgements

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

Author information

Correspondence to Thierry Viéville.

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Open Access This article is published under license to BioMed Central Ltd. This is an Open Access article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Cessac, B., Viéville, T. Revisiting time discretisation of spiking network models. BMC Neurosci 8, P76 (2007) doi:10.1186/1471-2202-8-S2-P76

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Keywords

  • Periodic Orbit
  • Neural Network Model
  • Neuron Model
  • Generic Regime
  • Condition Sensitivity