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

Abstract

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

Publisher's Note: Stationary and dynamical properties of information entropies in nonextensive systems [Phys. Rev. E77, 031133 (2008)]

“…Unfortunately, we cannot obtain analytic distributions in the Langevin model subjected to spatially correlated additive and multiplicative noise, because we have no analytic approaches to solve the relevant FPE, even for N = 2 [19]. It is necessary to develop an appropriate analytic method to solve the FPE including the spatial correlation in additive and multiplcative noise.…”

Stationary and dynamical properties of information entropies in nonextensive systems

“…[18], we obtained analytic expressions for the Tsallis entropy and the generalized Fisher entropy in spatially correlated nonextensive systems from the q-Gaussian-type distribution derived by the maximum-entropy method [18]. Unfortunately, we cannot obtain analytic distributions in the Langevin model subjected to spatially correlated additive and multiplicative noise, because we have no analytic approaches to solve the relevant FPE, even for N = 2 [19]. It is necessary to develop an appropriate analytic method to solve the FPE including the spatial correlation in additive and multiplcative noise.…”

“…where λ expresses the relaxation rate, and r and s are additional parameters. In the case of [β 2 + α 2 (r 2 − s 2 )] > 0, the stationary distribution is given by [19] p…”