Detecting nonstationarity and state transitions in a time series
Abstract
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/fα 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.
- Publication:
-
Physical Review E
- Pub Date:
- June 2001
- DOI:
- 10.1103/PhysRevE.63.066202
- Bibcode:
- 2001PhRvE..63f6202G
- Keywords:
-
- 05.45.Tp;
- 02.50.Fz;
- Time series analysis;
- Stochastic analysis