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

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

2006-03-06

arxiv.org/abs/cond-mat/0603115v6

Physica A 374 (2007) 585-599

Physics

Condensed Matter

Disordered Systems and Neural Networks

19 pages, 9 figures; accepted in Physica A with minor modifications

Scientific paper

10.1016/j.physa.2006.08.053

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.

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