Cooperative behavior in a jump diffusion model for a simple network of spiking neurons

Roberta Sirovich; Laura Sacerdote; Alessandro E. P. Villa

doi:10.3934/mbe.2014.11.385

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2014, Volume 11, Issue 2: 385-401. Doi: 10.3934/mbe.2014.11.385 open access

This issue Previous Article Demographic modeling of transient amplifying cell population growth Next Article

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: September 30, 2012

Revised: April 30, 2013

Published: September 2013

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Abstract

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

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Mathematics Subject Classification: 60G99, 60K40, 90B15, 92B20.

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