Explosive synchronization in weighted complex networks.

Area of Science:

• Complex Systems
• Network Science
• Nonlinear Dynamics

Background:

• Dynamical abrupt transitions in macroscopic systems are of significant interest.
• Understanding synchronization in complex networks is crucial for various scientific fields.

Purpose of the Study:

• To develop a practical weighting procedure to induce and enhance explosive, irreversible transitions to synchronization in phase oscillator networks.
• To investigate the control over hysteresis in synchronization transitions.

Main Methods:

• Combining dynamical local information on frequency mismatches with global graph topology.
• Utilizing a judicious and practical weighting procedure.
• Conducting extensive numerical and analytical investigations.

Main Results:

• The proposed weighting procedure effectively induces and enhances explosive synchronization.
• The method is valid and scalable across different frequency distributions and network types (homogeneous/heterogeneous).
• Both linear and nonlinear weighting functions were successful.
• Parametric control over the width and extent of the hysteretic region was achieved.

Conclusions:

• A novel and effective method for controlling explosive synchronization in complex networks has been demonstrated.
• The findings offer new possibilities for managing and controlling collective behaviors in networked systems.
• The procedure's scalability and adaptability suggest broad applicability in diverse synchronization phenomena.