Dynamical complexity measure to distinguish organized from disorganized dynamics

Area of Science:

• Complex Systems Analysis
• Dynamical Systems Theory
• Information Theory

Background:

• Characterizing complex dynamical systems is challenging.
• Existing metrics often fail to capture both predictability and structural organization.
• Distinguishing between organized and disorganized complexity requires a multifaceted approach.

Purpose of the Study:

• To introduce a novel metric for quantifying the complexity of dynamical systems.
• To differentiate between organized and disorganized complexity.
• To validate the metric's efficacy across diverse systems and applications.

Main Methods:

• Developed a complexity metric by combining permutation entropy (S_p) and a structurality indicator (Δ).
• Permutation entropy quantifies dynamical unpredictability.
• Structurality assesses the describability of the Poincaré section structure.
• Validated the metric using benchmark dissipative and conservative dynamical systems.

Main Results:

• The proposed metric successfully classifies the complexity of various dynamical systems.
• The (S_p, Δ) space effectively distinguishes between different types of complexity.
• Demonstrated the metric's utility as a biomarker for cardiac pathologies.
• Applied the metric to differentiate dynamical complexity in electrochemical dissolution processes.

Conclusions:

• The novel complexity metric offers a robust way to characterize dynamical systems.
• This approach provides a powerful tool for analyzing complex behaviors in diverse scientific fields.
• The metric shows promise for identifying pathological conditions and understanding material science phenomena.