Mean-field dynamics of a population of stochastic map neurons

Abstract

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.

arXiv comment12 pages, 11 figures

References in corpus (10)

• Modeling of Spiking-Bursting Neural Behavior Using Two-Dimensional Map
• Noise Induced Complexity: From Subthreshold Oscillations to Spiking in Coupled Excitable Systems
• Chaotic oscillations in a map-based model of neural activity
• Dynamical mean-field theory of spiking neuron ensembles: response to a single spike with independent noises
• Activation process in excitable systems with multiple noise sources: One and two interacting units
• Excitable elements controlled by noise and network structure
• Mean field approximation of two coupled populations of excitable units
• Mean-field dynamics of a random neural network with noise
• Evolving dynamical networks with transient cluster activity
• Persistence and failure of mean-field approximations adapted to a class of systems of delay-coupled excitable units