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Enhancing network synchronizability by strengthening a single node.

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Improving complex system stability requires efficient synchronizability. This study introduces an eigenvector-centrality-based scheme to enhance network synchronization by strengthening a single oscillator, outperforming traditional methods.

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Area of Science:

  • Complex Systems
  • Network Science
  • Nonlinear Dynamics

Background:

  • Achieving desired performance in complex dynamical systems at low cost is challenging.
  • Improving system synchronizability with limited coupling resources is crucial for engineering and biological networks.

Purpose of the Study:

  • To investigate how to efficiently improve network synchronizability by adding minimal coupling to a single oscillator.
  • To identify the optimal location for strengthening a node to maximize network synchronization.

Main Methods:

  • Utilized a complex network of coupled chaotic oscillators as a model system.
  • Developed a theoretical framework to determine the optimal node for strengthening based on eigenvector centrality.
  • Proposed and validated the eigenvector-centrality-based strengthening scheme through numerical simulations across various network models.

Main Results:

  • Theoretical analysis revealed that strengthening the oscillator corresponding to the eigenvector of the most unstable mode maximizes network synchronizability.
  • The proposed eigenvector-centrality-based scheme demonstrated superior performance compared to conventional centrality measures (betweenness, closeness, degree).
  • Numerical verification confirmed that the identified oscillator yields the best synchronization performance.

Conclusions:

  • The eigenvector-centrality-based strengthening scheme offers an efficient and effective method for enhancing synchronization in complex networks.
  • This approach provides a low-cost solution for improving the stability and performance of systems reliant on synchronous dynamics.