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Perfect synchronization in complex networks with higher-order interactions.

Sangita Dutta1, Prosenjit Kundu2, Pitambar Khanra3

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|September 19, 2023
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Summary
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Researchers developed a method for perfect synchronization in complex networks with higher-order interactions (HOIs) using the Sakaguchi-Kuramoto (SK) model. This analytical approach provides a stable frequency set for achieving synchrony and enhances network robustness.

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Area of Science:

  • Complex network theory
  • Nonlinear dynamics
  • Statistical physics

Background:

  • Achieving perfect synchronization in complex networks, especially with higher-order interactions (HOIs), is a significant challenge.
  • The Sakaguchi-Kuramoto (SK) model is a fundamental framework for studying synchronization phenomena.

Purpose of the Study:

  • To present a theoretical framework for achieving perfect synchronization in complex networks with HOIs.
  • To analytically derive a frequency set for targeted synchronization in the SK model with HOIs.

Main Methods:

  • Analytical derivation of a frequency set for perfect synchrony.
  • Numerical simulations on scale-free, random, and small-world networks.
  • Low-dimensional network reduction for stability analysis.
  • Introduction of Gaussian noise to assess robustness.

Main Results:

  • The analytically derived frequency set enables stable perfect synchronization at a desired point in the network.
  • The proposed frequency set is highly effective in achieving synchronization around the target point.
  • The synchronization state demonstrates stability and robustness against perturbations.

Conclusions:

  • The theoretical framework successfully provides a method for achieving and maintaining perfect synchronization in complex networks with HOIs.
  • The derived frequency set offers a robust and effective solution for synchronization control in various network topologies.