Dynamical Mean Field approximation of a canonical cortical model for studying inter-population synchrony
نویسندگان
چکیده
The goal of this paper is twofold, propose and explore a model to study the synchronization among populations in the canonical model of the neocortex proposed previously by [R.J. Douglas, K.A.C. Martin, A functional microcircuit for cat visual cortex. J. Physiol. 440(1991) 735–769]. For this, a model describing m N synapses of each m -population ( ) 1,2,3 m = is proposed. Each synapse is described by a system of 2 stochastic differential equations (SDEs). Then, by using the dynamical mean field approximation (DMA) [H. Hasegawa, Dynamical mean-field theory of spiking neuron ensembles: Response to a single spike with independent noises, Phys. Rev. E. (2003) 119.] the system of 2 m m N ∑ SDEs is reduced to 12 ordinary differential equations for the means and the second-order moments of global variables. The connectivity among populations is obtained by summarizing in the canonical model the detailed information from a quantitative description of the circuits formed in cat area 17 given in [T. Binzegger, R.J. Douglas, K.A. Martin, A Quantitative Map of the Circuit of Cat Primary Visual Cortex, J. Neurosci. 24 (2004) 84418453]. In the framework of the used DMA we propose a measure for inter-population synchronization. Simulations are carried out for exploring how inter-population synchrony is related to the variation of firing frequency of each population. Our results suggest that superficial pyramidal cluster appear to have a predominant influence on synchronization process among pyramidal populations as well as put forward the active role of inhibition in the rest of synchronizations between populations.
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