Detecting nonstationarity and state transitions in a time series

One cause of complexity in a time series may be due to nonstationarity and transience. In this paper, we analyze the nonstationarity and transience in a number of dynamical systems. We find that the nonstationarity in the metastable chaotic Lorenz system is due to nonrecurrence. The latter determines a lack of fractal structure in the signal. In ${1/f}^{\alpha }$ noise, we find that the associated correlation dimension are local graph dimensions calculated from sojourn points. We also design a transient Lorenz system with a slowly oscillating controlling parameter, and a transient Rossler system with a slowly linearly increasing parameter, with parameter ranges covering a sequence of chaotic dynamics with increased phase incoherence. State transitions, from periodic to chaotic, and vice versa, are identified, together with different facets of nonstationarity in each phase.