Synchronization induced by periodic inputs in finite N-unit bistable Langevin models: The augmented moment method

We have studied the synchronization induced by periodic inputs applied to a finite N-unit coupled bistable Langevin model which is subjected to cross-correlated additive and multiplicative noises. The effects on the synchronization of the system size (N), the coupling strength and the cross-correlation between additive and multiplicative noise have been investigated using the semi-analytical augmented moment method (AMM) which is a second-order moment approximation for local and global variables [H. Hasegawa, Phys. Rev. E 67 (2003) 041903]. A linear analysis of the stationary solution of the AMM equations shows that the stability is improved (degraded) by positive (negative) couplings. Results of the nonlinear bistable Langevin model are compared to those of the linear Langevin model.