Ordinal pattern-based complexity analysis of high-dimensional chaotic time series

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.