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Ayham Zaitouny1, David M Walker2, Michael Small1

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This study introduces the quadrant scan technique for analyzing recurrence plots to detect tipping points in dynamical systems. The quadrant scan effectively identifies state and dynamic transitions, even in complex, large, or multiscale datasets.

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Area of Science:

  • Dynamical systems analysis
  • Signal processing
  • Complex systems science

Background:

  • Transition detection is crucial across many scientific disciplines for understanding system changes.
  • Recurrence plots are a powerful tool for visualizing and analyzing dynamical systems.
  • Identifying tipping points is essential for predicting system behavior and potential shifts.

Purpose of the Study:

  • To investigate the quadrant scan technique for analyzing recurrence plots.
  • To identify tipping points in dynamical systems using the quadrant scan.
  • To develop and validate an extension of the quadrant scan for enhanced performance.

Main Methods:

  • Utilizing the quadrant scan technique on recurrence plots.
  • Analytically defining and proving the detection of state-transition and dynamic-transition.
  • Developing a weighted scheme to extend the standard quadrant scan.
  • Applying the technique to various temporal and non-temporal, multivariate, and large datasets.

Main Results:

  • Analytical proof of the quadrant scan's ability to detect both state and dynamic transitions.
  • Demonstration of the extended quadrant scan's effectiveness in overcoming standard limitations.
  • Successful application to diverse datasets, including non-temporal and multivariate data.
  • Capability to classify multiscale transitions shown through detailed examples.

Conclusions:

  • The quadrant scan technique is a robust method for identifying tipping points in dynamical systems.
  • The proposed extension enhances the technique's applicability to complex and large-scale data.
  • Quadrant scans offer a versatile approach for transition detection across various scientific domains.