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Mathematical models for the study of synchronization phenomena in neuronal networks

Abstract : The spike train, i.e. the sequence of the action potential timings of a single unit, is the usual data that is analyzed in electrophysiological recordings for the description of the firing pattern which is supposed to characterize a certain type of cell.. We present the results obtained describing the firing activity of a small network of neurons with a mathematical jump diffusion model. That is the membrane potential as a function of time is given by the sum of a stochastic diffusion process and two counting processes that provoke jumps of constant sizes at discrete random times. Different distributions are considered for such processes. Two main results emerge. The first one is that interspike intervals (ISI) histograms show more than one peak (multimodality) and exhibit a resonant like behavior. This fact suggests that in correspondence of each mode (i.e. the lag of the maxima) the cell has a higher probability of firing such that the the lags become characteristic times of the cell which could be modulated under physiological conditions. The second main result concerns the role of inhibition in neuronal coding. Indeed we show that the inhibitory inputs may facilitate the transmission of the spikes generated by the excitatory inputs. This fact suggests that inhibitory cells are not only involved in keeping balanced the excitability of the cell but that they may also play a key role in the information process. Such kind of models requires to improve the algorithms to simulate the first passage time through a threshold of a stochastic process. So that the second part of this manuscript is dedicated to a a purely theoretical study on multidimensional bridge processes.
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Contributor : Roberta Sirovich <>
Submitted on : Tuesday, May 16, 2006 - 12:44:43 PM
Last modification on : Friday, November 6, 2020 - 3:44:17 AM
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  • HAL Id : tel-00069125, version 1




Roberta Sirovich. Mathematical models for the study of synchronization phenomena in neuronal networks. Neurons and Cognition [q-bio.NC]. Université Joseph-Fourier - Grenoble I, 2006. English. ⟨tel-00069125⟩



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