An augmented moment method for stochastic ensembles with delayed couplings: II. FitzHugh-Nagumo model

Abstract

Dynamics of FitzHugh-Nagumo (FN) neuron ensembles with time-delayed couplings subject to white noises, has been studied by using both direct simulations and a semi-analytical augmented moment method (AMM) which has been proposed in a recent paper [H. Hasegawa, E-print: cond-mat/0311021]. For $N$-unit FN neuron ensembles, AMM transforms original $2N$-dimensional {\it stochastic} delay differential equations (SDDEs) to infinite-dimensional {\it deterministic} DEs for means and correlation functions of local and global variables. Infinite-order recursive DEs are terminated at the finite level $m$ in the level-$m$ AMM (AMM$m$), yielding $8(m+1)$-dimensional deterministic DEs. When a single spike is applied, the oscillation may be induced if parameters of coupling strength, delay, noise intensity and/or ensemble size are appropriate. Effects of these parameters on the emergence of the oscillation and on the synchronization in FN neuron ensembles have been studied. The synchronization shows the {\it fluctuation-induced} enhancement at the transition between non-oscillating and oscillating states. Results calculated by AMM5 are in fairly good agreement with those obtained by direct simulations.

15 pages, 3 figures; changed the title with correcting typos, accepted in Phys. Rev. E with some changes

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Cited by in corpus (7)

• 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
• Mean field approximation for noisy delay coupled excitable neurons
• Mean field approximation of two coupled populations of excitable units
• Generalized Rate-Code Model for Neuron Ensembles with Finite Populations
• Stationary and dynamical properties of finite $N$-unit Langevin models subjected to multiplicative noises
• Persistence and failure of mean-field approximations adapted to a class of systems of delay-coupled excitable units