Summary
International Symposium on Nonlinear Theory and its Applications
2010
Session Number:C3L-A
Session:
Number:C3L-A1
Linearity and nonlinearity within recurrence plots
Yoshito Hirata, Kazuyuki Aihara,
pp.577-580
Publication Date:2010/9/5
Online ISSN:2188-5079
Summary:
Recurrence plots are widely used for analysing time series generated from complex systems. While it is argued that the taurecurrence rate is similar to the autocorrelation, it is still not clear which characteristics within recurrence plots represent their linear and nonlinear properties. In this paper, we observe how fast the number of diagonal lines decreases when their length increases. We found that in linear stochastic systems, the logarithm of the number scales exactly, while in typical nonlinear deterministic systems, the decreasing rate of the number tends to approach from the above. We illustrate our finding with numerical examples.