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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.

Chaos (Woodbury, N.Y.)
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Summary
This summary is machine-generated.

This study introduces a fractional multiplex higher-order network model. It demonstrates achieving intra-layer, inter-layer, and complete synchronization using Lyapunov methods and fractional inequalities.

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Area of Science:

  • Complex Networks
  • Nonlinear Dynamics
  • Fractional Calculus

Background:

  • Multiplex networks involve multiple layers of interactions.
  • Higher-order interactions capture group dynamics.
  • Synchronization is crucial for network function.

Purpose of the Study:

  • To establish a fractional multiplex higher-order network model.
  • To investigate synchronization phenomena within this model.
  • To analyze intra-layer, inter-layer, and complete synchronization.

Main Methods:

  • Development of a fractional multiplex higher-order network model.
  • Application of the Lyapunov direct method.
  • Utilization of fractional inequalities and a Lyapunov function.

Main Results:

  • Demonstration of intra-layer synchronization.
  • Proof of inter-layer synchronization.
  • Confirmation of complete synchronization in the network.

Conclusions:

  • The proposed model successfully achieves various synchronization types.
  • Theoretical results are validated by numerical simulations.
  • The study contributes to understanding complex network dynamics.