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Mirroring of synchronization in a bi-layer master-slave configuration of Kuramoto oscillators.

Chaos (Woodbury, N.Y.)·2022
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Effect of clustering on Turing instability in complex networks.

Samana Pranesh1, Devanand Jaiswal2, Sayan Gupta1,3

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Turing instability in complex networks depends on more than just network topology. Nodal clustering is also crucial for predicting Turing patterns, especially in real-world networks.

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Area of Science:

  • Complex networks
  • Mathematical biology
  • Network science

Background:

  • Turing instability in complex networks is linked to Laplacian matrix eigenvalues and network topology.
  • Previous studies highlighted the dependence on degree distribution and eigenvalues.

Purpose of the Study:

  • To investigate the role of nodal clustering in Turing instability beyond eigenvalue dependence.
  • To analyze the influence of clustering on Turing pattern formation across various network topologies.

Main Methods:

  • Analytical and numerical simulations were employed.
  • The study utilized S1/H2 hyperbolic geometric networks to model real-world clustering.
  • Analysis included Laplacian eigenvector localization properties.

Main Results:

  • Nodal clustering was identified as a critical factor, not just network topology or eigenvalues.
  • Distinct signatures in Laplacian eigenvector localization were found to identify Turing patterns.
  • The S1/H2 model successfully represented clustering in random and scale-free networks.

Conclusions:

  • Network topology and Laplacian eigenvalues are insufficient for predicting Turing instability.
  • Nodal clustering is a vital global network measure for understanding Turing patterns.
  • Eigenvector localization analysis offers a method for detecting Turing patterns in complex networks.