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A discrete time neural network model with spiking neurons

Rigorous results on the spontaneous dynamics

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Abstract

We derive rigorous results describing the asymptotic dynamics of a discrete time model of spiking neurons introduced in Soula et al. (Neural Comput. 18, 1, 2006). Using symbolic dynamic techniques we show how the dynamics of membrane potential has a one to one correspondence with sequences of spikes patterns (“raster plots”). Moreover, though the dynamics is generically periodic, it has a weak form of initial conditions sensitivity due to the presence of a sharp threshold in the model definition. As a consequence, the model exhibits a dynamical regime indistinguishable from chaos in numerical experiments.

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Authors and Affiliations

  1. INRIA, 2004 Route des Lucioles, 06902, Sophia-Antipolis, France

    B. Cessac

  2. INLN, 1361 Route des Lucioles, 06560, Valbonne, France

    B. Cessac

  3. Université de Nice, Parc Valrose, 06000, Nice, France

    B. Cessac

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  1. B. Cessac
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Cessac, B. A discrete time neural network model with spiking neurons. J. Math. Biol. 56, 311–345 (2008). https://doi.org/10.1007/s00285-007-0117-3

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  • DOI: https://doi.org/10.1007/s00285-007-0117-3

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