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The influence of noise on synchronous dynamics in a diluted neural network

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  • di Volo, Matteo
  • Livi, Roberto

Abstract

We study the influence of noise on the dynamics of a simple model of excitatory leaky integrate – and – fire neurons in a diluted network. The stochastic process amounts to a random walk with boundaries acting on the external current, whose average value plays the role of a control parameter identifying different dynamical phases. Above a given threshold value one observes a gaussian statistics of synchronous firing events, that changes to an asymmetric long-tail distribution below threshold. For uncorrelated noise the distribution below threshold exhibits an exponential tail for large rare events, while for strongly correlated noise the long-tail turns to a power-law. This interesting dynamical scenario is shown to persist also when short-term plasticity is introduced in the model. Synchronous firing events change to population bursts and the model with plasticity is shown to reproduce quantitatively what observed in in vitro experiments. We also discuss the persistence of this scenario in the thermodynamic limit.

Suggested Citation

  • di Volo, Matteo & Livi, Roberto, 2013. "The influence of noise on synchronous dynamics in a diluted neural network," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 54-61.
    • Handle: RePEc:eee:chsofr:v:57:y:2013:i:c:p:54-61
    DOI: 10.1016/j.chaos.2013.08.012
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    References listed on IDEAS

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    1. Jorge F Mejias & Hilbert J Kappen & Joaquin J Torres, 2010. "Irregular Dynamics in Up and Down Cortical States," PLOS ONE, Public Library of Science, vol. 5(11), pages 1-13, November.
    2. Volman, Vladislav & Baruchi, Itay & Persi, Erez & Ben-Jacob, Eshel, 2004. "Generative modelling of regulated dynamical behavior in cultured neuronal networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(1), pages 249-278.
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