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Dynamical mean-field theory of noisy spiking neuron ensembles: Application to the Hodgkin-Huxley model | | Hideo Hasegawa
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25 Feb 2003 | | Journal: | Phys. Rev. E 68 (2003) 041909 | | Subject: | Disordered Systems and Neural Networks; Neurons and Cognition | cond-mat.dis-nn q-bio.NC | | Affiliation: | Tokyo Gakugei Univ. | | Abstract: | A dynamical mean-field approximation (DMA) previously proposed by the present author [H. Hasegawa, Phys. Rev E {f 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 The original $KN$-dimensional {it stochastic} DEs have been replaced by $K(K+2)$-dimensional {it deterministic} DEs expressed in terms of means and the second-order moments of {it local} and {it global} variables: the fourth-order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. | | Source: | arXiv, cond-mat/0302502 | | Other source: | [GID 743770] pmid14682975 | | Services: | Forum | Review | PDF | Favorites | |
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