Fig. 3. (a) Kaplan–Yorke dimension DKYDKY for the Lorenz96 system, Eq. (1), with different system size N . The RP based measures (b) DET and (c) DTDT reveal a similar variation with the N as DKYDKY. Averaged values for 20 different initial states are presented. The standard deviations of the measures for the different initial conditions are presented by the error bars.Figure optionsDownload full-size imageDownload as PowerPoint slide
3. Recurrence plot analysis
RP quantification may be suitable for a simpler estimation of the dynamical properties. An RP Ri,j=Θ(ε−‖x→i−x→j‖) YM-155 a binary matrix R representing the time points j when a state x→i at time i recurs  ( Fig. 4). The recurrence criterion is usually defined as a spatial distance between two states x→i and x→j is falling below a threshold ε . Besides the ability to discuss the visual aspect of an RP, several quantification approaches are based on this matrix. The diagonal line structures in an RP correspond to periods of parallel evolution of two segments of the phase space trajectory. The scaling of the length distribution of such lines is related to the K2K2 entropy. A good proxy for this is measuring the inverse of the length of the longest diagonal line 1/Lmax1/Lmax, withequation(3)Lmax=argmaxlHD(l), and l the length of the diagonal lines, and HD(l)HD(l) the length distribution of diagonal lines in R .