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Area of Science:

  • Complex Systems Science
  • Network Science
  • Statistical Physics

Background:

  • Real-world systems often comprise interdependent networks with complex, multiple-dependency relationships.
  • Understanding these dependencies is crucial for designing robust and resilient infrastructure.
  • Existing models often simplify dependencies, limiting their applicability to realistic scenarios.

Purpose of the Study:

  • To develop a mathematical framework for analyzing interdependent networks with multiple-to-multiple node dependencies.
  • To investigate the percolation and cascading failure dynamics in such networks.
  • To assess the impact of coupling strength and connectivity density on system resilience.

Main Methods:

  • Development of a generalized mathematical framework for multiple interdependent networks.
  • Application of percolation theory to analyze network behavior.
  • Analytical and numerical studies of cascading failure processes, giant component size, and critical thresholds.
  • Simulations on coupled Erdős-Rényi and scale-free network models.

Main Results:

  • The system exhibits a discontinuous phase transition dependent on coupling strength.
  • Analytical results for the giant component size and critical threshold were obtained and validated by simulations.
  • Increased coupling strength and connectivity density enhance system resilience and ease of defense.

Conclusions:

  • The proposed framework accurately models complex dependencies in real-world systems.
  • Interdependent network resilience can be significantly improved by optimizing coupling parameters.
  • The findings offer insights for designing more robust and resilient interdependent systems.