Stochastic bifurcation in FitzHugh-Nagumo ensembles subjected to additive and/or multiplicative noises

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. 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 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). PACS No. 05.40.-a 05.45.-a 84.35.+i 87.10.+e