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ScanLag: High-throughput Quantification of Colony Growth and Lag Time
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Cluster lag synchronization and control for multiplex and directed network systems.

Shanrong Lin1, Xiwei Liu2

  • 1School of Information and Intelligent Science, Donghua University, Shanghai 201620, China; Department of Computer Science and Technology, and the Key Laboratory of Embedded System and Service Computing, Ministry of Education, Tongji University, Shanghai 201804, China; Department of Applied Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada.

ISA Transactions
|March 20, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces cluster lag synchronization (CLSyn) for complex multiplex and directed network systems (MDNS). New methods improve synchronization and control, enhancing network stability and performance.

Keywords:
Adaptive couplingCluster lag synchronization and controlInner and outer additive matricesMultiplex and directed networks

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Area of Science:

  • Complex Networks
  • Control Theory
  • Synchronization

Background:

  • Multiplex and directed network systems (MDNS) present unique challenges for synchronization.
  • Existing methods for cluster lag synchronization (CLSyn) have limitations.

Purpose of the Study:

  • To propose and investigate cluster lag synchronization (CLSyn) for MDNS.
  • To develop novel control strategies for achieving CLSyn in these networks.
  • To extend CLSyn concepts to include cluster complete and anticipated synchronization.

Main Methods:

  • A novel model for MDNS incorporating directed outer matrices and negative inner matrices.
  • Rearranging variable order technique for analyzing synchronization with time lags.
  • Development of pinning control and adaptive strength synchronization rules.
  • Application to multiplex and directed reaction-diffusion network systems (MDRDNS).

Main Results:

  • A generalized concept of CLSyn is introduced.
  • Effective synchronization rules under pinning control and adaptive strength are derived.
  • Conditions for CLSyn and pinning control in MDRDNS are established.
  • Numerical simulations validate the theoretical findings.

Conclusions:

  • The proposed methods effectively achieve CLSyn in MDNS.
  • The study advances the understanding and control of synchronization in complex networks.
  • The findings have implications for designing stable and robust network systems.