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Synchronization patterns: from network motifs to hierarchical networks.

Sanjukta Krishnagopal1,2, Judith Lehnert3, Winnie Poel3

  • 1Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany sanju33@gmail.com.

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Summary
This summary is machine-generated.

We explored synchronization in fractal networks of Stuart-Landau oscillators, revealing a direct link between hierarchical network topology and dynamics. This allows predicting large network behavior from small motifs.

Keywords:
fractal topologyhierarchical networksoscillation deathpartial synchronization

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Area of Science:

  • Cybernetical Physics
  • Complex Systems
  • Network Science

Background:

  • Fractal and hierarchical network topologies are relevant for modeling complex systems, including neural networks.
  • Understanding synchronization patterns in coupled oscillators is crucial for various scientific disciplines.
  • Previous research suggested symmetric coupling prevents oscillation death.

Purpose of the Study:

  • To investigate complex synchronization patterns in networks of coupled Stuart-Landau oscillators with fractal connectivities.
  • To analyze the interplay between hierarchical network topology and network dynamics.
  • To develop a method for predicting the dynamics of large hierarchical networks.

Main Methods:

  • Developed three models of hierarchical networks with fractal properties.
  • Introduced an analytical eigensolution method to study network dynamics.
  • Analyzed synchronization patterns including cluster synchronization and partial amplitude death.

Main Results:

  • Demonstrated a direct correlation between hierarchical topology and corresponding hierarchical dynamics.
  • Showed that oscillation death can be induced even with symmetric coupling in these networks.
  • Established that small network motifs can predict the dynamics of arbitrarily large hierarchical networks.

Conclusions:

  • Hierarchical networks exhibit predictable hierarchical dynamics, bridging mesoscale motifs and macroscopic network behavior.
  • The findings offer new insights into synchronization phenomena and network dynamics in fractal systems.
  • This work advances the understanding of complex systems by linking network structure to emergent dynamics.