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Recurrence condensation during critical transitions in complex systems.

Manaswini Jella1,2, Induja Pavithran2,3, Vishnu R Unni4

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Summary
This summary is machine-generated.

This study introduces recurrence analysis to detect critical transitions in complex systems, like turbulent fluids. The method, termed "recurrence condensation," identifies shifts from chaotic to periodic behavior, even in noisy data.

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Area of Science:

  • Complex Systems Dynamics
  • Fluid Mechanics
  • Nonlinear Dynamics

Background:

  • Critical transitions in complex systems can lead to catastrophic failures in natural and engineered systems.
  • Detecting these critical points is challenging, especially in noisy, high-dimensional systems.
  • Turbulent fluid systems exhibit complex dynamics that are difficult to predict and control near critical points.

Purpose of the Study:

  • To investigate critical transitions from chaotic to periodic oscillations in turbulent fluid systems using recurrence analysis.
  • To develop a method for detecting critical points in noisy systems with gradual transitions.
  • To term and quantify the observed phenomenon of 'recurrence condensation'.

Main Methods:

  • Utilized recurrence plots (RPs) and recurrence quantification measures (RQMs) on time series data from a turbulent fluid system.
  • Analyzed the evolution of recurrence patterns from disordered to ordered structures.
  • Quantified 'recurrence condensation' using measures like recurrence time, determinism, entropy, laminarity, and trapping time.

Main Results:

  • Recurrence plots showed a distinct progression indicating a shift from multiple time scales to a dominant single time scale ('recurrence condensation').
  • Recurrence quantification measures collapsed to a single dominant time scale, confirming the transition.
  • Recurrence measures exhibited power-law scaling near the critical point, allowing for precise detection of the critical parameter value.

Conclusions:

  • Recurrence analysis, specifically 'recurrence condensation,' is an effective method for detecting critical transitions in noisy, complex systems.
  • The method successfully identified the critical point in a synthetic noisy Hopf bifurcation model, coinciding with the bifurcation point.
  • This approach offers valuable insights for identifying poorly defined transition points in various scientific and engineering domains.