Synchronization detection using spatial ordinal partitions in networks.

Area of Science:

• Complex Systems
• Network Science
• Dynamical Systems Theory

Background:

• Identifying collective behaviors in coupled dynamical systems is crucial for understanding complex network dynamics.
• Existing methods may struggle with partially synchronized states or networks with non-uniform connectivity.

Purpose of the Study:

• To develop and validate a robust methodology for detecting synchronous regions and classifying collective behaviors in networks of coupled dynamical systems.
• To extend the analysis to networks where traditional spatiotemporal analysis is infeasible.

Main Methods:

• Utilizing ordinal patterns of spatial configurations of neighboring oscillators to detect synchronization at each time point.
• Employing permutation entropy and forbidden sequence cardinality for the classification of collective behaviors.
• Applying the method to a ring network of coupled logistic maps and subsequently to a network with random connections.

Main Results:

• The method successfully detects synchronous regions and confirms previous findings on collective behavior identification.
• It accurately identifies the boundaries of synchronous regions in partially synchronized networks.
• Demonstrated efficacy on a randomly connected network, proving useful when spatiotemporal plots are not feasible.

Conclusions:

• The proposed methodology offers a robust approach to analyzing synchronization and collective behaviors in complex networks.
• It provides a powerful tool for characterizing network states, particularly in scenarios with partial synchronization or complex topologies.