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Cluster synchronization: From single-layer to multi-layer networks
Cun Ma1, Qirui Yang1, Xiaoqun Wu1
1School of Mathematics and Statistics, Wuhan University, Hubei 430072, China.
Chaos (Woodbury, N.Y.)
|January 3, 2020
Summary
This study investigates cluster synchronization in multilayer networks, finding that external network structure and inter-layer connections significantly impact synchronization. The new "cluster synchronizability" metric quantifies this network ability.
Area of Science:
- Network Science
- Complex Systems Analysis
- Synchronization Phenomena
Background:
- Cluster synchronization is prevalent in single-layer and multilayer networks.
- Understanding external influences on synchronization is crucial for real-world applications.
Purpose of the Study:
- To explore how an external layer impacts cluster synchronization in a multilayer network.
- To introduce and utilize "cluster synchronizability" to measure a network's ability to achieve synchronization.
- To analyze the effects of external layer topology and inter-layer connection patterns.
Main Methods:
- Numerical simulations were employed to study cluster synchronization.
- Analysis involved varying external layer structures (community networks, different densities).
- Investigated three connection patterns: positive, negative, and random correlations.
Main Results:
- External layer topology significantly influences cluster synchronizability.
- Different network densities and community structures in the external layer affect synchronization.
- Inter-layer connection patterns (positive, negative, random) demonstrably impact cluster synchronization.
Conclusions:
- Multilayer network structure and inter-layer coupling are key determinants of cluster synchronization.
- The concept of "cluster synchronizability" provides a valuable metric for network analysis.
- Further theoretical work is needed for a comprehensive understanding of cluster synchronization in multilayer networks.
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