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Load fluctuations in complex networks are finite in weakly heterogeneous systems above a density threshold. However, they diverge in strongly heterogeneous networks due to hub activity, impacting system stability.

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Area of Science:

  • Complex systems science
  • Network theory
  • Statistical physics

Background:

  • Synchronizing individual activities is crucial for complex system stability.
  • Understanding load fluctuations in relation to network topology is vital but limited to regular lattices.
  • Heterogeneous networks, common in real-world systems, present unique challenges for load balancing.

Purpose of the Study:

  • To investigate load fluctuation dynamics in heterogeneous networks.
  • To analyze the impact of link density and degree exponents on load fluctuations.
  • To understand the mechanisms driving load fluctuation divergence in complex systems.

Main Methods:

  • Analysis of load fluctuations in the largest-connected components of heterogeneous networks.
  • Systematic variation of network link density and degree exponents.
  • Examination of the relationship between load fluctuation, spectral dimension, and node degree.

Main Results:

  • Load fluctuation becomes finite in weakly heterogeneous networks above a critical link density threshold.
  • In strongly heterogeneous networks, load fluctuation diverges even when the spectral dimension exceeds 2.
  • Hub nodes and their neighbors exhibit large local fluctuations that drive anomalous divergence in the overall system.

Conclusions:

  • The behavior of load fluctuations differs significantly between weakly and strongly heterogeneous networks.
  • Hubs play a critical role in generating diverging fluctuations in heterogeneous systems.
  • The developed analysis framework aids in understanding and controlling fluctuations in real-world complex systems.