Stationary and dynamical properties of finite $N$-unit Langevin models subjected to multiplicative noises

TL;DR

This paper analyzes the stationary and dynamical behaviors of finite N-unit Langevin models with multiplicative noise, using the augmented moment method and Fokker-Planck equations, revealing diverse stationary distributions influenced by noise and inputs.

Contribution

It extends previous work by applying the augmented moment method to study effects of coupling and noise on Langevin models, comparing diffusive and sigmoid couplings.

Findings

AMM results agree with direct simulations for time-dependent variables

Stationary distributions vary significantly with multiplicative noise and inputs

Differences between diffusive and sigmoid couplings are characterized

Abstract

We have studied the finite $N$-unit Langevin model subjected to multiplicative noises, by using the augmented moment method (AMM), as a continuation of our previous paper [H. Hasegawa, J. Phys. Soc. Jpn. {\bf 75} (2006) 033001]. Effects of couplings on stationary and dynamical properties of the model have been investigated. The difference and similarity between the results of diffusive and sigmoid couplings are studied in details. Time dependences of average and fluctuations in local and global variables calculated by the AMM are in good agreement with those of direct simulations (DSs). We also discuss stationary distributions of local and global variables with the use of the Fokker-Planck equation (FPE) method and DSs. It is demonstrated that stationary distributions show much variety when multiplicative noise and external inputs are taken into account.