Analytical Description of Recurrence Plots of White Noise and Chaotic Processes

Marco Thiel; M Carmen Romano; Jurgen Kurths

Analytical Description of Recurrence Plots of White Noise and Chaotic Processes

Marco Thiel, M Carmen Romano , Jurgen Kurths

University of Potsdam

Research output: Chapter in Book/Report/Conference proceeding › Published conference contribution

Abstract

We present an analytical description of the distribution of diagonal lines in Recurrence Plots (RPs) for white noise and chaotic systems, and find that the latter one is linked to the correlation entropy. Further we identify two scaling regions in the distribution of diagonals for oscillatory chaotic systems that are hinged to two prediction horizons and to the geometry of the attractor. These scaling regions cannot be observed with the Grassberger-Procaccia algorithm. Finally, we propose methods to estimate dynamical invariants from RPs.

Original language	English
Title of host publication	Izvestiya VUZ Applied Nonlinear Dynamics
Place of Publication	Saratov, Russia
Publisher	Saratov State University
Pages	20-30
Number of pages	11
Volume	11
Edition	3
Publication status	Published - Feb 2003

Publication series

Name	Izvestiya VUZ. Applied Nonlinear Dynamics
Publisher	Saratov State University
ISSN (Print)	0869-6632
ISSN (Electronic)	2542-1905

Bibliographical note

Acknowledgements
We thanks Dieter Armbruster, Annette Witt, Udo Schwarz, Norbert Marwan for the fruitful discussions. The project was supported by the "DFG-Schwerpunktprogrmm 1114"

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Analytical Description of Recurrence Plots of White Noise and Chaotic Processes. / Thiel, Marco ; Romano , M Carmen; Kurths, Jurgen.
Izvestiya VUZ Applied Nonlinear Dynamics. Vol. 11 3. ed. Saratov, Russia: Saratov State University, 2003. p. 20-30 (Izvestiya VUZ. Applied Nonlinear Dynamics).

Research output: Chapter in Book/Report/Conference proceeding › Published conference contribution

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AU - Romano , M Carmen

AU - Kurths, Jurgen

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PY - 2003/2

Y1 - 2003/2

N2 - We present an analytical description of the distribution of diagonal lines in Recurrence Plots (RPs) for white noise and chaotic systems, and find that the latter one is linked to the correlation entropy. Further we identify two scaling regions in the distribution of diagonals for oscillatory chaotic systems that are hinged to two prediction horizons and to the geometry of the attractor. These scaling regions cannot be observed with the Grassberger-Procaccia algorithm. Finally, we propose methods to estimate dynamical invariants from RPs.

AB - We present an analytical description of the distribution of diagonal lines in Recurrence Plots (RPs) for white noise and chaotic systems, and find that the latter one is linked to the correlation entropy. Further we identify two scaling regions in the distribution of diagonals for oscillatory chaotic systems that are hinged to two prediction horizons and to the geometry of the attractor. These scaling regions cannot be observed with the Grassberger-Procaccia algorithm. Finally, we propose methods to estimate dynamical invariants from RPs.

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M3 - Published conference contribution

VL - 11

T3 - Izvestiya VUZ. Applied Nonlinear Dynamics

SP - 20

EP - 30

BT - Izvestiya VUZ Applied Nonlinear Dynamics

PB - Saratov State University

CY - Saratov, Russia

ER -

Analytical Description of Recurrence Plots of White Noise and Chaotic Processes

Abstract

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