Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems

Area of Science:

• Complex Systems Science
• Network Science
• Dynamical Systems Theory

Background:

• Time series analysis is crucial for understanding complex systems.
• Existing ordinal partition methods offer insights but can be refined.
• Network representations provide a novel perspective on time series dynamics.

Purpose of the Study:

• To generalize the ordinal partition time series to network transformation algorithm.
• To introduce time delay embedding for partition element selection.
• To investigate the sensitivity of network structures to underlying system dynamics.

Main Methods:

• Generalized ordinal partition time series to network transformation.
• Time delay embedding for selecting partition elements.
• Network construction based on temporal succession (Markov chain).
• Application to Rössler system and experimental diode resonator data.

Main Results:

• Periodic dynamics yield ring structures; chaotic dynamics yield band/tube structures.
• Network measures (mean out-degree, variance) track dynamical changes.
• Network size, path length, and diameter detect an interior crisis in experimental data.

Conclusions:

• The generalized algorithm generates networks sensitive to system dynamics.
• Network properties can effectively characterize time series behavior.
• This approach offers a powerful tool for analyzing complex dynamical systems.