2006/10/02 by Hideo Hasegawa, Hasegawa, Hideo
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Random Matrices and Applications #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0610028
23 pages, 13 figures, accepted in Physica D with minor changes
openalex publication_date 2006/10/02 · arxiv created 2007/08/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We have studied the dynamical properties of finite N-unit FitzHugh-Nagumo (FN) ensembles subjected to additive and/or multiplicative noises, reformulating the augmented moment method (AMM) with the Fokker-Planck equation (FPE) method [H. Hasegawa, J. Phys. Soc. Jpn. \bf 75, 033001 (2006)]. In the AMM, original 2N-dimensional stochastic equations are transformed to eight-dimensional deterministic ones, and the dynamics is described in terms of averages and fluctuations of local and global variables. The stochastic bifurcation is discussed by a linear stability analysis of the \it deterministic AMM equations. The bifurcation transition diagram of multiplicative noise is rather different from that of additive noise: the former has the wider oscillating region than the latter. The synchronization in globally coupled FN ensembles is also investigated. Results of the AMM are in good agreement with those of direct simulations (DSs).