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

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 preceding paper [H. Hasegawa, Phys. Rev E xx, yyyy (2004)]. For N -unit FN neuron ensembles, AMM transforms original 2N -dimensional stochastic delay differential equations (SDDEs) to infinitedimensional 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 (AMMm), yielding 8(m + 1)-dimensional deterministic DEs. When a single spike is applied, the oscillation may be induced when 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 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. PACS numbers 87.10.+e 84.35.+i 05.45.-a 07.05.Mh Typeset using REVTEX e-mail: [email protected]