Optimal estimation of recurrence structures from time series

Recurrent temporal dynamics is a phenomenon observed frequently in high-dimensional complex systems and its detection is a challenging task. Recurrence quantification analysis utilizing recurrence plots may extract such dynamics, however it still encounters an unsolved pertinent problem: the optimal...

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Bibliographic Details
Published in:Europhysics letters 2016-05, Vol.114 (3), p.38003-38003
Main Authors: beim Graben, Peter, Sellers, Kristin K., Fröhlich, Flavio, Hutt, Axel
Format: Article
Language:English
Subjects:
05.10.-a
05.45.Tp
89.75.Fb
Animals
Complex systems
Dimensional analysis
Dynamic structural analysis
Dynamical systems
Dynamics
Estimation
Goodness of fit
Lorenz system
Markov chains
Nonlinear dynamics
Optimization
Stochasticity
Systems analysis
Thresholds
Time series
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Summary:Recurrent temporal dynamics is a phenomenon observed frequently in high-dimensional complex systems and its detection is a challenging task. Recurrence quantification analysis utilizing recurrence plots may extract such dynamics, however it still encounters an unsolved pertinent problem: the optimal selection of distance thresholds for estimating the recurrence structure of dynamical systems. The present work proposes a stochastic Markov model for the recurrent dynamics that allows for the analytical derivation of a criterion for the optimal distance threshold. The goodness of fit is assessed by a utility function which assumes a local maximum for that threshold reflecting the optimal estimate of the system's recurrence structure. We validate our approach by means of the nonlinear Lorenz system and its linearized stochastic surrogates. The final application to neurophysiological time series obtained from anesthetized animals illustrates the method and reveals novel dynamic features of the underlying system. We propose the number of optimal recurrence domains as a statistic for classifying an animals' state of consciousness.
ISSN:0295-5075
1286-4854
DOI:10.1209/0295-5075/114/38003