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Node differentiation dynamics along the route to synchronization in complex networks.

Christophe Letellier1, Irene Sendiña-Nadal2,3, Ludovico Minati4,5

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Nodes in synchronized networks differentiate dynamically, regardless of global structure. Higher connectivity initially reduces complexity, while weak coupling increases it, with hubs synchronizing first. Strong coupling shows hierarchical differentiation.

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Area of Science:

  • Complex Systems
  • Network Science
  • Nonlinear Dynamics

Background:

  • Decades of synchronization research focused on global coherence.
  • Individual node dynamics during synchronization remain under-explored.

Purpose of the Study:

  • To investigate the dynamical development of individual nodes during network synchronization.
  • To understand how node complexity evolves irrespective of global network topology.

Main Methods:

  • Analysis of dynamical systems within networks.
  • Examination of node behavior across different connectivity classes.
  • Study across various nonlinear dynamics models and coupling functions.

Main Results:

  • Nodes in the same degree class exhibit similar dynamical differentiation paths.
  • Initial coupling reduces complexity, more so in highly connected nodes.
  • Weak coupling increases complexity, peaking first in hubs.
  • Strong coupling reveals hierarchical differentiation, with low-degree nodes showing greater complexity departure.

Conclusions:

  • Node dynamical differentiation is a universal feature during synchronization.
  • This differentiation depends on node connectivity and coupling strength.
  • Findings offer insights for network identification and inference strategies.