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The synchrony and variability have been discussed of the coupled Langevinmodel subjected to spatially correlated additive and multiplicative noise. Wehave employed numerical simulations and the analytical augmented-moment methodwhich is the second-order moment method for local and global variables [H.Hasegawa, Phys. Rev. E {\bf 67}, 041903 (2003)]. It has been shown that thesynchrony of an ensemble is increased (decreased) by a positive (negative)spatial correlation in both additive and multiplicative noise. Although thevariability for local fluctuations is almost insensitive to spatialcorrelations, that for global fluctuations is increased (decreased) by positive(negative) correlations. When a pulse input is applied, the synchrony isincreased for the correlated multiplicative noise, whereas it may be decreasedfor correlated additive noise coexisting with uncorrelated multiplicativenoise. An application of our study to neuron ensembles has demonstrated thepossibility that information is conveyed by the variance and synchrony in inputsignals, which accounts for some neuronal experiments.

Synchrony and variability induced by spatially correlated additive and multiplicative noise in the coupled Langevin model