Synchronizability of two-layer correlation networks.

Area of Science:

• Complex networks
• Network science
• Statistical physics

Background:

• Two-layer correlation networks are crucial in modeling complex systems.
• Understanding network synchronizability is key to network function and stability.
• Interlayer linking patterns significantly influence network dynamics.

Purpose of the Study:

• To investigate the synchronizability of two-layer correlation networks with positive correlation (PC) and negative correlation (NC) linking patterns.
• To analyze the impact of linking patterns, linking strength, and network size on network stability.
• To identify optimal linking strengths for maximizing synchronizability while minimizing cost.

Main Methods:

• Analysis of the Laplacian matrix eigenvalues for network stability.
• Application of the master stability function.
• Theoretical analysis and numerical verification of network synchronizability.

Main Results:

• Negative correlation (NC) linking patterns exhibit superior synchronizability compared to positive correlation (PC) patterns.
• Linking patterns, strength, and network size profoundly influence synchronizability.
• Optimal intralayer and interlayer linking strengths were identified for maximizing synchronizability and minimizing cost.

Conclusions:

• The study provides a theoretical framework for understanding and enhancing synchronizability in two-layer networks.
• NC linking patterns offer a more effective strategy for achieving network synchronization.
• Findings offer insights for designing and optimizing general multiplex correlation networks.