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Driving-based generalized synchronization in two-layer networks via pinning control.

Di Ning1, Xiaoqun Wu1, Jun-an Lu1

  • 1School of Mathematics and Statistics, Wuhan University, Hubei 430072, China.

Chaos (Woodbury, N.Y.)
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Summary

This study explores generalized synchronization (GS) in two-layer complex networks using pinning control. Researchers found that network density and coupling strength influence the number and type of nodes needed for effective synchronization.

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Area of Science:

  • Complex Networks
  • Systems Science
  • Control Theory

Background:

  • Synchronization is crucial in complex systems.
  • Generalized synchronization (GS) describes harmonious coexistence between networks.
  • Real-world networks often exhibit interdependent dynamics.

Purpose of the Study:

  • Investigate GS in two-layer complex networks with unidirectional coupling.
  • Apply pinning control to achieve synchronization.
  • Develop a theoretical framework and practical guidance for engineers.

Main Methods:

  • Utilized the auxiliary-system approach for analysis.
  • Designed drive and response network layers with unidirectional inter-layer coupling.
  • Employed pinning control strategies.

Main Results:

  • Presented a sufficient condition for achieving GS via pinning control.
  • Demonstrated that GS is achievable through numerical simulations.
  • Found that fewer pinned nodes are needed as response layer density increases.

Conclusions:

  • The study offers a practical method for achieving harmonious coexistence in complex systems.
  • Optimal pinning strategies depend on intra-layer coupling strength and node degree.
  • Findings facilitate system selection and reduce control costs.