FIG. 2.

(Color online) (a) and (b) Scaling laws for the Rössler system for two different randomly chosen time points taken over a short time series of length N = 4500. See Eq. (6) for red lines (lines fitted to the dots) and Eq. (8) for blue lines (lines fitted to the open squares). Note that $\frac{{\beta }_j}{{\alpha }_j}\to 1$ here in the absence of dynamical transitions in the model. The embedding parameters used were m = 10 and L = 15. (c) and (d) Scaling laws in the logistic map for two different randomly chosen time points over a short time series of length N = 4500. See Eq. (6) for red lines and Eq. (8) for blue lines. Note again that $\frac{{\beta }_j}{{\alpha }_j}\to 1$ as there are no dynamical transitions. The embedding parameters used were m = 3 and L = 2. We also observe the fluctuations in the values of exponents α and β, possibly caused by the shortness of these time series and numerical error in the evolution of the dynamics.