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We have studied the synchronization induced by periodic inputs applied to thefinite $N$-unit coupled bistable Langevin model which is subjected tocross-correlated additive and multiplicative noises. Effects on thesynchronization of the system size ($N$), the coupling strength and thecross-correlation between additive and multiplicative noises have beeninvestigated with the use of the semi-analytical augmented moment method (AMM)which is the second-order moment approximation for local and global variables[H. Hasegawa, Phys. Rev. E {\bf 67} (2003) 041903]. A linear analysis of thestationary solution of AMM equations shows that the stability is improved(degraded) by positive (negative) couplings. Results of the nonlinear bistableLangevin model are compared to those of the linear Langevin model.

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