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Area of Science:

  • Nonlinear dynamics
  • Chaos theory
  • Time series analysis

Background:

  • The complexity-entropy (CE) plane is widely used to differentiate stochastic (noise) and deterministic chaotic signals.
  • Its effectiveness has primarily been shown for low-dimensional systems.

Purpose of the Study:

  • To assess the utility of the CE plane for high-dimensional chaotic dynamics.
  • To evaluate its performance on complex systems like Lorenz-96 and Kuramoto-Sivashinsky equations.

Main Methods:

  • Applied the CE plane method to time series from high-dimensional systems (Lorenz-96, Hénon map, Mackey-Glass, Kuramoto-Sivashinsky).
  • Utilized phase-randomized surrogate data for comparison.
  • Analyzed behavior with varying lag and pattern lengths.

Main Results:

  • High-dimensional deterministic chaotic time series and stochastic surrogate data occupied similar regions on the CE plane.
  • Their representations exhibited comparable behavior across different lag and pattern lengths.
  • Classification using CE plane position proved challenging and potentially misleading.

Conclusions:

  • The CE plane's effectiveness is limited for distinguishing high-dimensional chaos from noise.
  • Surrogate data tests based on entropy and complexity provide significant results in most cases.
  • Careful interpretation is needed when applying CE plane analysis to complex, high-dimensional data.