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Synchronization on fractional multiplex higher-order networks
Chenjun Ma1, Weiyuan Ma1, Xiaoqin Wang1
1School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730000, China.
Abstract:
This paper explores the synchronization problem in fractional multiplex higher-order networks. Initially, a fractional multiplex higher-order network model is established, which seamlessly integrates multiplex structures with higher-order interactions. Subsequently, by leveraging a well-crafted Lyapunov function, the Lyapunov direct method, and fractional inequalities, it is demonstrated that the fractional multiplex higher-order network can achieve intra-layer synchronization, inter-layer synchronization, and complete synchronization. Finally, the theoretical findings are validated through two numerical examples featuring a simplicial complex or hypergraph structures within the intra-layer network.
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