Synchronization analyze of k-uniform hyper-networks

Area of Science:

• Complex Systems
• Network Science
• Mathematical Physics

Background:

• Hyper-networks excel at modeling multivariate relationships.
• Synchronization dynamics in complex hyper-networks remain under-explored due to structural complexity.

Purpose of the Study:

• To propose a Kuramoto model tailored for k-uniform hyper-networks.
• To analyze the synchronization properties of these hyper-networks based on structural parameters.

Main Methods:

• Developed a generalized Laplacian matrix expression for k-uniform hyper-networks.
• Quantified synchronization using the eigenvalue ratio of the generalized Laplacian matrix.
• Investigated synchronization in Erdős-Rényi (ER) random, Watts-Strogatz (NW) small-world, and Barabási-Albert (BA) scale-free hyper-networks.

Main Results:

• Synchronization is influenced by both hyper-network structure and parameters.
• Synchronization increases with node size in ER random hyper-networks but decreases in NW small-world and BA scale-free hyper-networks.
• Increased uniformity enhances synchronization across all tested hyper-network types.

Conclusions:

• The proposed model provides a framework for understanding synchronization in k-uniform hyper-networks.
• Hyper-network synchronization is sensitive to uniformity, node size, and hyper-clustering coefficients, exhibiting distinct behaviors across different network models.