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Synchronization and equitable partitions in weighted networks.

Manuela A D Aguiar1, Ana Paula S Dias2

  • 1Faculdade de Economia, Centro de Matemática, Universidade do Porto, Rua Dr Roberto Frias, 4200-464 Porto, Portugal.

Chaos (Woodbury, N.Y.)
|August 3, 2018
PubMed
Summary
This summary is machine-generated.

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This study extends coupled cell network theory to weighted networks, revealing connections between synchrony subspaces and balanced relations. These findings link two research areas, enhancing the understanding of network dynamics.

Area of Science:

  • Dynamical Systems and Network Theory
  • Mathematical Biology
  • Graph Theory

Background:

  • Coupled cell network formalism traditionally uses nonnegative integer connection values.
  • Existing literature lacks a unified framework for weighted networks in this context.

Purpose of the Study:

  • To demonstrate the natural extension of the coupled cell network formalism to weighted networks.
  • To establish a correspondence between existing concepts and those in weighted network analysis.
  • To link two distinct but related strands of network literature.

Main Methods:

  • Applying central concepts and results of the existing formalism to weighted networks.
  • Analyzing synchrony subspaces and balanced relations in weighted coupled cell networks.

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  • Establishing equivalences between synchrony subspaces/balanced relations and cluster of synchrony/equitable partitions.

    • Main Results:

    • The coupled cell network formalism effectively accommodates weighted networks.
    • Key results concerning synchrony subspaces and balanced relations are generalized to weighted networks.
    • A direct correspondence is shown between synchrony subspaces and cluster of synchrony, and balanced relations and equitable partitions.

    Conclusions:

    • The generalized formalism provides a unified framework for analyzing both unweighted and weighted coupled cell networks.
    • This work bridges the gap between different theoretical approaches in network science.
    • The findings are applicable to a broader range of network dynamics and systems.