title: Dynamics of moment neuronal networks.
abstract: A theoretical framework is developed for moment neuronal networks (MNNs). Within this framework, the behavior of the system of spiking neurons is specified in terms of the first- and second-order statistics of their interspike intervals, i.e., the mean, the variance, and the cross correlations of spike activity. Since neurons emit and receive spike trains which can be described by renewal--but generally non-Poisson--processes, we first derive a suitable diffusion-type approximation of such processes. Two approximation schemes are introduced: the usual approximation scheme (UAS) and the Ornstein-Uhlenbeck scheme. It is found that both schemes approximate well the input-output characteristics of spiking models such as the IF and the Hodgkin-Huxley models. The MNN framework is then developed according to the UAS scheme, and its predictions are tested on a few examples.
authors.affiliation: Department of Mathematics, Hunan Normal University, 410081 Changsha, People's Republic of China.
authors.forename: Jianfeng
authors.initials: J
authors.lastname: Feng
authors.forename: Yingchun
authors.initials: Y
authors.lastname: Deng
authors.forename: Enrico
authors.initials: E
authors.lastname: Rossoni
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000465:Algorithms; D000818:Animals; D001683:Biological Clocks / Q000502:physiology*; D003198:Computer Simulation; D006801:Humans; D007700:Kinetics; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*; D009435:Synaptic Transmission / Q000502:physiology*