Mean-field dynamics of a population of stochastic map neurons

We analyze the emergent regimes and the stimulus-response relationship of a population of noisy map neurons by means of a mean-field model, derived within the framework of cumulant approach complemented by the Gaussian closure hypothesis. It is demonstrated that the mean-field model can qualitativel...

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Bibliographic Details
Published inPhysical review. E Vol. 96; no. 1-1; p. 012226
Main Authors Franović, Igor, Maslennikov, Oleg V, Bačić, Iva, Nekorkin, Vladimir I
Format Journal Article
LanguageEnglish
Published United States 01.07.2017
Subjects
Action Potentials
Animals
Models, Neurological
Neurons - physiology
Periodicity
Stochastic Processes
Synapses - physiology
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Summary:We analyze the emergent regimes and the stimulus-response relationship of a population of noisy map neurons by means of a mean-field model, derived within the framework of cumulant approach complemented by the Gaussian closure hypothesis. It is demonstrated that the mean-field model can qualitatively account for stability and bifurcations of the exact system, capturing all the generic forms of collective behavior, including macroscopic excitability, subthreshold oscillations, periodic or chaotic spiking, and chaotic bursting dynamics. Apart from qualitative analogies, we find a substantial quantitative agreement between the exact and the approximate system, as reflected in matching of the parameter domains admitting the different dynamical regimes, as well as the characteristic properties of the associated time series. The effective model is further shown to reproduce with sufficient accuracy the phase response curves of the exact system and the assembly's response to external stimulation of finite amplitude and duration.
ISSN:2470-0053
DOI:10.1103/PhysRevE.96.012226