Dynamics and synchronization of noisy neuron ensembles with time-delayed couplings

Dynamics of FitzHugh-Nagumo (FN) neuron ensembles with 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 by the author [H. Hasegawa, E-print: cond-mat/0311021]. For N -unit FN neuron ensembles, AMM transforms original 2N -dimensional stochastic delay differential equations (SDDE) to infinite-dimensional deterministic DEs for the correlation functions of local and global variables. Infinite-order recursive DEs are terminated at the level 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 neuron ensembles have been studied. The synchronization shows the fluctuation-induced enhancement at the transition between non-oscillating and oscillating states. Results calculated by the level-5 AMM are in fairly good agreement with those obtained by direct simulations. PACS numbers 87.10.+e 84.35.+i 05.45.-a 07.05.Mh Typeset using REVTEX e-mail: [email protected]