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Updated: Jul 29, 2025

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Global Topological Synchronization on Simplicial and Cell Complexes.

Timoteo Carletti1, Lorenzo Giambagli1,2, Ginestra Bianconi3,4

  • 1Department of Mathematics and naXys, Namur Institute for Complex Systems, University of Namur, Rue Grafé 2, B5000 Namur, Belgium.

Physical Review Letters
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Summary
This summary is machine-generated.

Higher-order networks can synchronize topological signals. Cell complexes enable synchronization across all dimensions, overcoming topological obstructions that hinder simplicial complexes with odd-dimensional signals.

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Area of Science:

  • Complex systems
  • Network science
  • Nonlinear dynamics

Background:

  • Topological signals on higher-order networks are gaining interest.
  • Collective phenomena of these signals are under-explored.
  • Understanding synchronization in these complex structures is crucial.

Purpose of the Study:

  • To determine conditions for global synchronization of topological signals.
  • To investigate synchronization on simplicial and cell complexes.
  • To identify factors enabling or impeding synchronization.

Main Methods:

  • Combining topology and nonlinear dynamics.
  • Analyzing signals on simplicial complexes.
  • Analyzing signals on cell complexes.

Main Results:

  • Topological obstructions prevent odd-dimensional signals from synchronizing on simplicial complexes.
  • Cell complexes can overcome topological obstructions.
  • Signals of any dimension can achieve global synchronization in certain cell complex structures.

Conclusions:

  • The type of complex network (simplicial vs. cell) dictates synchronization possibilities.
  • Cell complexes offer greater flexibility for global synchronization of topological signals.
  • Future research can explore specific cell complex structures for enhanced synchronization.