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

TL;DR

This study investigates how periodic inputs induce synchronization in finite-size coupled bistable Langevin systems with cross-correlated noises, using a semi-analytical augmented moment method to analyze effects of system size, coupling, and noise correlation.

Contribution

The paper introduces a semi-analytical augmented moment method to analyze synchronization in finite bistable Langevin models with cross-correlated noises, highlighting effects of system parameters.

Findings

Positive coupling improves stability; negative coupling degrades it.

Synchronization is influenced by system size, coupling strength, and noise correlation.

Comparison between nonlinear and linear Langevin models shows consistent trends.

Abstract

We have studied the synchronization induced by periodic inputs applied to the finite $N$-unit coupled bistable Langevin model which is subjected to cross-correlated additive and multiplicative noises. Effects on the synchronization of the system size ($N$), the coupling strength and the cross-correlation between additive and multiplicative noises have been investigated 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 the stationary solution of 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.