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Extended recurrence plot and quantification for noisy continuous dynamical systems.

Dadiyorto Wendi1, Norbert Marwan2

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Summary
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Noise in time series data disrupts recurrence plots (RP) and recurrence quantification analysis (RQA). This study introduces an extended RQA approach to reliably analyze noisy signals, improving determinism measures.

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Area of Science:

  • Dynamical Systems Analysis
  • Time Series Signal Processing
  • Nonlinear Dynamics

Background:

  • Noise in observational time series data poses a significant challenge for constructing reliable recurrence plots (RP) and performing recurrence quantification analysis (RQA).
  • Noise-induced disruptions and deviations in diagonal lines of RPs can bias traditional RQA measures, leading to inaccurate conclusions about system dynamics.
  • Increasing the recurrence threshold to connect discontinuous lines results in thicker lines, artificially inflating RQA metrics like Determinism and Laminarity.

Purpose of the Study:

  • To propose an extended recurrence quantification analysis (RQA) approach capable of accurately analyzing continuous dynamical systems with noisy time series data.
  • To develop methods that account for disrupted and deviated diagonal lines in recurrence plots caused by signal noise.
  • To introduce an extended local minima approach for RP construction to mitigate artificial structures and improve RQA.

Main Methods:

  • Development of an extended RQA approach utilizing a sliding diagonal window with a minimal window size to tolerate deviated lines.
  • Incorporation of a specified minimal lag between connected points within the sliding window.
  • Proposal of an extended local minima approach for recurrence plot construction to reduce artificial block and vertical structures.

Main Results:

  • The proposed extended RQA approach provides a more reliable determinism indicator for noisy signals where conventional RQA fails.
  • The sliding diagonal window method effectively tolerates noise-induced line deviations, preserving the integrity of RQA measures.
  • The extended local minima approach helps to reduce artificial increases in RQA metrics such as Laminarity (LAM).

Conclusions:

  • The developed extended RQA methodology offers a robust solution for analyzing dynamical systems in the presence of significant time series noise.
  • This approach enhances the accuracy of determinism estimation from noisy data, overcoming limitations of conventional RQA.
  • The extended local minima method further refines RP construction, leading to more accurate quantification of system dynamics.