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Complex network synchronizability: analysis and control.

Zhisheng Duan1, Guanrong Chen, Lin Huang

  • 1State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, People's Republic of China. duanzs@pku.edu.cn

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 1, 2008
PubMed
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Network synchronizability depends on inner linking and topological matrices. Adding edges can improve synchronizability, especially for networks with disconnected complementary graphs, leading to design methods for enhanced network performance.

Area of Science:

  • Network Science
  • Graph Theory
  • Systems Engineering

Background:

  • Identical node dynamics in networks can exhibit varying synchronizability despite similar structural parameters.
  • Network synchronizability is influenced by factors beyond basic graph properties like average distance and degree distribution.

Purpose of the Study:

  • To identify key factors governing network synchronizability.
  • To investigate the impact of adding edges on network synchronizability.
  • To propose a design method for enhancing network synchronizability.

Main Methods:

  • Analysis of network synchronizability using inner linking matrices and eigenvalues of topological matrices.
  • Comparative study of graph structures with identical parameters but different synchronizabilities.

Related Experiment Videos

  • Examination of edge addition effects on networks, particularly those with disconnected complementary graphs.

    • Main Results:

    • Network synchronizability is determined by the inner linking matrix and eigenvalues of the topological matrix.
    • Adding edges can increase or decrease synchronizability; it never decreases for networks with disconnected complementary graphs.
    • Networks with unbounded synchronized regions are simpler to analyze.

    Conclusions:

    • The inner linking matrix and topological eigenvalues are critical for network synchronizability.
    • Strategic edge addition, particularly in networks with disconnected complementary graphs, can enhance synchronizability.
    • A design method for rank 1 inner linking matrices yields unbounded synchronized regions, simplifying analysis and improving synchronizability.