Unveiling the Connectivity of Complex Networks Using Ordinal Transition Methods

Area of Science:

• Complex Systems Science
• Network Science
• Nonlinear Dynamics

Background:

• Ordinal measures are useful for correlated data series analysis.
• Understanding information flow and network structure in dynamical systems using ordinal methods is underexplored.
• Existing methods struggle to differentiate network roles during synchronization.

Purpose of the Study:

• To compare ordinal permutation entropy with a new permutation entropy measure based on ordinal transition matrices.
• To assess the effectiveness of these measures in identifying the topological roles of nodes in networked chaotic systems.
• To demonstrate the applicability of the novel method to real-world time series data.

Main Methods:

• Calculated ordinal permutation entropy for time series data.
• Developed and applied permutation entropy based on ordinal transition probability matrices.
• Tested measures on networked chaotic Rössler systems.
• Validated the method using experimental data from nonlinear oscillator networks.

Main Results:

• The permutation entropy of the ordinal transition matrix significantly outperformed standard ordinal permutation entropy.
• The proposed method effectively discriminated the topological roles of nodes in networked chaotic systems.
• The method demonstrated robustness in analyzing experimental time series data.

Conclusions:

• Permutation entropy of ordinal transition matrices offers a powerful new tool for network analysis.
• This approach can uncover network structure from time series data, even with unknown underlying networks.
• The method is applicable to diverse real-world systems exhibiting correlations and network structures.