Fluctuations in complex networks with variable dimensionality and heterogeneity.

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.