Dynamical mean-field theory of noisy spiking neuron ensembles: Application to the Hodgkin-Huxley model

Abstract

A dynamical mean-field approximation (DMA) previously proposed by the present author [H. Hasegawa, Phys. Rev E {\bf 67}, 041903 (2003)] has been extended to ensembles described by a general noisy spiking neuron model. Ensembles of $N$-unit neurons, each of which is expressed by coupled $K$-dimensional differential equations (DEs), are assumed to be subject to spatially correlated white noises. The original $KN$-dimensional {\it stochastic} DEs have been replaced by $K(K+2)$-dimensional {\it deterministic} DEs expressed in terms of means and the second-order moments of {\it local} and {\it global} variables: the fourth-order contributions are taken into account by the Gaussian decoupling approximation. Our DMA has been applied to an ensemble of Hodgkin-Huxley (HH) neurons (K=4), for which effects of the noise, the coupling strength and the ensemble size on the response to a single-spike input have been investigated. Results calculated by DMA theory are in good agreement with those obtained by direct simulations.

21 pages, 3 figures, revised the text

References in corpus (3)

• Dynamical mean-field theory of spiking neuron ensembles: response to a single spike with independent noises
• Stochastic Resonance of Ensemble Neurons for Transient Spike Trains: A Wavelet Analysis
• Spike-Train Responses of a Pair of Hodgkin-Huxley Neurons with Time-Delayed Couplings

Cited by in corpus (12)

• Noise Induced Complexity: From Subthreshold Oscillations to Spiking in Coupled Excitable Systems
• Synchronizations in small-world networks of spiking neurons: Diffusive versus sigmoid couplings
• Dynamical mean-filed approximation to small-world networks of spiking neurons: From local to global, and/or from regular to random couplings
• An augmented moment method for stochastic ensembles with delayed couplings: I. Langevin model
• An augmented moment method for stochastic ensembles with delayed couplings: II. FitzHugh-Nagumo model
• Mean field approximation for noisy delay coupled excitable neurons
• Generalized Rate-Code Model for Neuron Ensembles with Finite Populations
• $N$-dependent Multiplicative-Noise Contributions in Finite $N$-unit Langevin Models: Augmented Moment Approach
• Stationary and dynamical properties of finite $N$-unit Langevin models subjected to multiplicative noises
• Population rate codes carried by mean, fluctuation and synchrony of neuronal firings
• Graded persisting activity of heterogeneous neuron ensembles subject to white noises
• Synchronization induced by periodic inputs in finite $N$-unit bistable Langevin models: The augmented moment method