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How to enhance adaptive synchronization capability via higher-order network structures?

Qiuyue Zhao1,2, Lilan Tu1,2, Jia Hu1,2

  • 1Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan 430065, China.

Chaos (Woodbury, N.Y.)
|February 19, 2026
PubMed
Summary
This summary is machine-generated.

Reducing control costs and enhancing synchronization in higher-order networks is crucial. Smaller network sizes and coupling strengths lower costs, while increasing 2-simplices improves adaptive synchronization, especially in Erdős-Rényi simplicial complex networks.

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Area of Science:

  • Complex Networks
  • Network Synchronization
  • Control Theory

Background:

  • Higher-order dynamic networks, incorporating first-order (edges) and second-order (2-simplices) interactions, present complex synchronization challenges.
  • Reducing control costs and enhancing synchronization capability are critical issues in network science and engineering.

Purpose of the Study:

  • To derive a sufficient condition for adaptive synchronization in higher-order dynamic networks using Lyapunov stability theory.
  • To investigate the impact of network structure and parameters on control costs and synchronization performance.
  • To compare the adaptive synchronization capabilities and robustness of different higher-order network models.

Main Methods:

  • Development of a theoretical framework based on Lyapunov stability theory to ensure adaptive synchronization.
  • Construction and analysis of three distinct higher-order network models: Erdős-Rényi simplicial complex (ERSC), Watts-Strogatz simplicial complex (WSSC), and Barabási-Albert simplicial complex (BASC).
  • Analysis of first- and second-order degree distributions within these network models.
  • Validation through numerical simulations to assess theoretical findings.

Main Results:

  • Smaller network scales and coupling strengths effectively reduce control costs and energy consumption across all investigated network types.
  • Erdős-Rényi simplicial complex (ERSC) networks exhibit superior adaptive synchronization capability with an increased number of 2-simplices.
  • Watts-Strogatz simplicial complex (WSSC) networks demonstrate greater robustness compared to ERSC and Barabási-Albert simplicial complex (BASC) networks when varying coupling strengths or the number of 2-simplices.

Conclusions:

  • The study provides a theoretical condition for adaptive synchronization in higher-order networks, offering insights into cost reduction and performance enhancement.
  • Network topology and parameter choices significantly influence synchronization efficiency and control costs, with ERSC and WSSC showing distinct advantages.
  • Findings suggest that optimizing network structure, specifically the number of higher-order simplices and coupling strengths, is key to achieving efficient and robust adaptive synchronization.