Splayed Recurrence Analysis of Iterated Dynamical Systems

2016 ◽  
pp. 137-153
Author(s):  
Charles L. Webber
Keyword(s):  
Dynamical Systems ◽  
Recurrence Analysis

LOCAL MINIMA-BASED RECURRENCE PLOTS FOR CONTINUOUS DYNAMICAL SYSTEMS

2011 ◽  
Vol 21 (04) ◽  
pp. 1065-1075 ◽  
Author(s):  
AARON P. SCHULTZ ◽  
YONG ZOU ◽  
NORBERT MARWAN ◽  
MICHAEL T. TURVEY
Keyword(s):  
Dynamical Systems ◽  
Lorenz System ◽  
Distance Matrix ◽  
Redundant Information ◽  
Local Minima ◽  
Recurrence Plots ◽  
Orthogonal Direction ◽  
Recurrence Analysis ◽  
Line Segments ◽  
Temporal Correlations

A major issue in using recurrence plots (RPs) to study dynamical systems is the choice of neighborhood size for thresholding the distance matrix that creates the plot. This is particularly important for continuous dynamical systems as temporal correlations of the trajectory might provide redundant information for recurrence analysis. We suggest an alternative procedure for creating RPs using the local minima provided by the distance profile, which approximately corresponds to the recurrence information in the orthogonal direction. The local minima-based thresholding yields a clean RP of minimized line thickness, that is compared to the plot obtained by the standard radius bases thresholding. New definitions of line segments arising from the local minima-based method are outlined, which yield consistent results with those derived from standard methods. Our preliminary comparison suggests that the newly introduced thresholding technique is more sensitive to small changes in a system's dynamics. We demonstrate our method via the chaotic Lorenz system without the loss of generality.

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