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An augmented moment method for stochastic ensembles with delayed couplings: II. FitzHugh-Nagumo model | | Hideo Hasegawa
; | | Date: |
8 Nov 2003 | | Journal: | Phys. Rev. E 70 (2004) 021912 | | Subject: | Disordered Systems and Neural Networks; Statistical Mechanics; Quantitative Methods | cond-mat.dis-nn cond-mat.stat-mech q-bio.QM | | Affiliation: | Tokyo Gakugei Univ. | | 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. | | Source: | arXiv, cond-mat/0311183 | | Services: | Forum | Review | PDF | Favorites | |
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