Abstract
This paper describes how to characterize convergence properties of the synchronization system which consists of two identical nonlinear dynamical systems linked by a common noisy input only. We consider two types of input: the harmonic and random (HR) forcing and the narrow-band random (NR) forcing. Statistical linearization approach enables us to characterize the convergence properties while Liapunov exponents, which is a well-known identifier to provide a necessary condition of occurrence of the synchronization, fail to characterize them. The result shows that it is possible to detect the condition of slow convergence as multi-valued solutions of moment equations of the target system.
