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Mathematical Biosciences and Engineering

2014, Volume 11, Issue 2: 385-401. doi: 10.3934/mbe.2014.11.385
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Cooperative behavior in a jump diffusion model for a simple network of spiking neurons

  • 1.
    Department of Mathematics "G. Peano", University of Torino, Via Carlo Alberto 10, 10123 Torino
  • 2.
    Grenoble Institute of Neuroscience Inserm UMRS 836, University Joseph Fourier Grenoble
  • Received: 01 October 2012 Accepted: 29 June 2018 Published: 01 October 2013

  • MSC : 60G99, 60K40, 90B15, 92B20.

  • The distribution of time intervals between successivespikes generated by a neuronal cell --the interspike intervals(ISI)-- may reveal interesting features of the underlyingdynamics. In this study we analyze the ISI sequence --thespike train-- generated by a simple network of neurons whose outputactivity is modeled by a jump-diffusion process. We prove that,when specific ranges of the involved parameters are chosen, it is possible toobserve multimodal ISI distributions which reveal that the modelednetwork fires with more than one single preferred time interval.Furthermore, the system exhibits resonance behavior, withmodulation of the spike timings by the noise intensity. We also show that inhibition helps the signal transmission between theunits of the simple network.

    Citation: Roberta Sirovich, Laura Sacerdote, Alessandro E. P. Villa. Cooperative behavior in a jump diffusion model for a simple network of spiking neurons[J]. Mathematical Biosciences and Engineering, 2014, 11(2): 385-401. doi: 10.3934/mbe.2014.11.385

    Related Papers:

  • The distribution of time intervals between successivespikes generated by a neuronal cell --the interspike intervals(ISI)-- may reveal interesting features of the underlyingdynamics. In this study we analyze the ISI sequence --thespike train-- generated by a simple network of neurons whose outputactivity is modeled by a jump-diffusion process. We prove that,when specific ranges of the involved parameters are chosen, it is possible toobserve multimodal ISI distributions which reveal that the modelednetwork fires with more than one single preferred time interval.Furthermore, the system exhibits resonance behavior, withmodulation of the spike timings by the noise intensity. We also show that inhibition helps the signal transmission between theunits of the simple network.


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  • © 2014 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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