Recurrence Time Statistics for Chaotic Systems and Their Applications

By studying recurrence time statistics for chaotic systems, we identify two different types of recurrences and develop scaling laws relating the mean recurrence time to the information dimension of the chaotic attractor. We then design two novel and simple ways of using the recurrence time statistics for analyzing transient as well as nonstationary time series. We show that the methods are capable of detecting nonstationarity due to drift of parameters, locating bifurcations, telling the periodicity of major transient periodic motions, and other types of changes in the dynamics.