Analysis of complex time series from coupled map lattices

Özet

Detecting deterministic behaviour in systems with a large number of coupled degrees of freedom is a challenging task [1]. In order to successfully employ the embedding theorem or to compute quantities like generalized dimensions in the re¬constructed phase space from scalar observations, one needs dauntingly long time series. Moreover, most of the methods for analysing chaotic signals are tailored to relatively low dimensional systems and give ambiguous results when the number of dimensions of the attractor is large. We introduce discrete topological variables and an autocorrelation function to examine intermittent time series for deterministic behaviour. For time series obtained from a single arbitrary point on a one-dimensional coupled map lattice [2] (with the chain length going up to 256), we find that the autocorrelation function we define gives a clear indication of deterministic behaviour in the intermittent regime. We relate the largest Lyapunov exponent to the modulation frequency of the autocorrelation function. The latter quantity is obtained from the power spectrum of the autocorrelation function.