Synchronizability of Multi-Layer Variable Coupling Windmill-Type Networks

Jian Zhu, Da Huang, Haijun Jiang, Jicheng Bian and Zhiyong Yu
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Jian Zhu: Department of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi 830023, China
Da Huang: Department of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi 830023, China
Haijun Jiang: College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China
Jicheng Bian: Department of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi 830023, China
Zhiyong Yu: College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China

Mathematics, 2021, vol. 9, issue 21, 1-14

Abstract: The system model on synchronizability problem of complex networks with multi-layer structure is closer to the real network than the usual single-layer case. Based on the master stability equation (MSF), this paper studies the eigenvalue spectrum of two k-layer variable coupling windmill-type networks. In the case of bounded and unbounded synchronization domain, the relationships between the synchronizability of the layered windmill-type networks and network parameters, such as the numbers of nodes and layers, inter-layers coupling strength, are studied. The simulation of the synchronizability of the layered windmill-type networks are given, and they verify the theoretical results well. Finally, the optimization schemes of the synchronizability are given from the perspective of single-layer and multi-layer networks, and it was found that the synchronizability of the layered windmill-type networks can be improved by changing the parameters appropriately.

Keywords: multi-layer networks; windmill-type; coupling strength; synchronizability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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