One main challenge in constructing a reliable recurrence plot (RP) and, hence, its quantification [recurrence quantification analysis (RQA)] of a continuous dynamical system is the induced noise that is commonly found in observation time series. This induced noise is known to cause disrupted and deviated diagonal lines despite the known deterministic features and, hence, biases the diagonal line based RQA measures and can lead to misleading conclusions. Although discontinuous lines can be further connected by increasing the recurrence threshold, such an approach triggers thick lines in the plot. However, thick lines also influence the RQA measures by artificially increasing the number of diagonals and the length of vertical lines [e.g., Determinism () and Laminarity () become artificially higher]. To take on this challenge, an extended RQA approach for accounting disrupted and deviated diagonal lines is proposed. The approach uses the concept of a sliding diagonal window with minimal window size that tolerates the mentioned deviated lines and also considers a specified minimal lag between points as connected. This is meant to derive a similar determinism indicator for noisy signal where conventional RQA fails to capture. Additionally, an extended local minima approach to construct RP is also proposed to further reduce artificial block structures and vertical lines that potentially increase the associated RQA like LAM. The methodology and applicability of the extended local minima approach and equivalent measure are presented and discussed, respectively.
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August 2018
Research Article|
August 30 2018
Extended recurrence plot and quantification for noisy continuous dynamical systems
Special Collection:
Recurrence Quantification Analysis for Understanding Complex Systems
Dadiyorto Wendi;
Dadiyorto Wendi
1
Institute of Earth and Environmental Science, University of Potsdam
, Potsdam-Golm 14476, Germany
2
Potsdam Institute for Climate Impact Research (PIK)
, Potsdam 14412, Germany
3
Section 5.4 Hydrology, GFZ German Research Centre for Geosciences
, Potsdam 14473, Germany
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Norbert Marwan
Norbert Marwan
2
Potsdam Institute for Climate Impact Research (PIK)
, Potsdam 14412, Germany
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Chaos 28, 085722 (2018)
Article history
Received:
February 09 2018
Accepted:
May 02 2018
Citation
Dadiyorto Wendi, Norbert Marwan; Extended recurrence plot and quantification for noisy continuous dynamical systems. Chaos 1 August 2018; 28 (8): 085722. https://doi.org/10.1063/1.5025485
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