Recurrence plots for characterizing random dynamical systems

The recurrence plot was originally proposed for visualizing time series data. As plots have mainly been used analyzing generated from nonlinear deterministic systems, it is not well known whether they can be applied to gain insight into a random dynamical system, in which stochastic components play central role. In this study, we demonstrate that provide new viewpoints the stochasticity underlying dynamics. particular, present three theorems: first theorem demonstrates eventually establish one-to-one correspondence with joint set of initial conditions and inputs if dynamics expansive topologically transitive; second distinguishes systems; third enables shorter series. Moreover, propose test based on plot. theorems are verified by numerical examples as real datasets.