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Spike Spectra for Recurrences.

K Hauke Kraemer1, Frank Hellmann1, Mehrnaz Anvari1

  • 1Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association, 14473 Potsdam, Germany.

Entropy (Basel, Switzerland)
|November 24, 2022
PubMed
Summary
This summary is machine-generated.

We developed the inter-spike spectrum, a new method for analyzing time series data. This technique reveals dominant periodicities in complex systems, offering a powerful alternative to traditional power spectrum analysis.

Keywords:
bifurcationsdecompositionfrequency analysisrecurrence analysis

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Area of Science:

  • Complex Systems Analysis
  • Time Series Analysis
  • Nonlinear Dynamics

Background:

  • Recurrence analysis quantifies cyclical patterns in high-dimensional time series.
  • The τ-recurrence rate captures temporal correlations but lacks a clear spectral interpretation.
  • Existing methods lack a satisfactory analogue to the power spectrum for recurrence analysis.

Purpose of the Study:

  • Introduce a novel method to decompose the τ-recurrence rate.
  • Develop an analogue to the power spectrum for recurrence analysis.
  • Reveal dominant periodicities in underlying time series.

Main Methods:

  • Decomposition of the τ-recurrence rate using an over-complete basis of Dirac combs.
  • Application of sparsity regularization techniques.
  • Analysis of various time series examples.

Main Results:

  • The novel decomposition is termed the 'inter-spike spectrum'.
  • The inter-spike spectrum reveals dominant periodicities, analogous to the power spectrum.
  • The method correctly identifies patterns and transitions in diverse systems.
  • The inter-spike spectrum demonstrates robustness to measurement noise.

Conclusions:

  • The inter-spike spectrum provides a meaningful spectral analysis for recurrence quantification.
  • This method enhances the understanding of periodicities in high-dimensional time series.
  • The technique is applicable across various complex systems and robust to noise.