Stationary and dynamical properties of finite N-unit Langevin models with additive and multiplicative noises

We have studied stationary and dynamical properties of finite N -unit Langevin model subjected to additive and multiplicative noises, by using the Fokker-Planck equation and the augmented moment method (AMM) which was previously proposed by the author. The probability distribution in the stationary states may have much variety when multiplicative noises and external inputs are taken into account. Time dependences of average and fluctuations in local and global variables calculated by the AMM are in good agreement with those of direct simulations. It is demonstrated that the Langevin model applied to neuronal ensembles may yield the interspike-interval distributions which are non-Gaussians including gamma, inverseGaussian-like and log-normal-like distributions. PACS No. 05.10.Gg, 05.45.-a, 84.35.+i Electronic address: [email protected]