Percolation Transitions in Edge-Coupled Interdependent Networks with Reinforced Inter-Layer Links

Area of Science:

• Network Science
• Complex Systems
• Statistical Physics

Background:

• Cascading failures in interdependent networks are a critical concern.
• Existing research primarily focuses on node coupling, neglecting edge-coupled interactions.
• The impact of reinforced inter-layer links in edge-coupled networks remains unexplored.

Purpose of the Study:

• To develop a theoretical framework for analyzing percolation in edge-coupled interdependent networks with reinforced inter-layer links.
• To investigate the role of reinforced inter-layer links in preventing network collapse and controlling phase transitions.
• To compare the effectiveness of inter-layer link reinforcement with intra-layer strategies.

Main Methods:

• Development of a theoretical framework for percolation models.
• Derivation of analytical expressions for giant/finite components and percolation thresholds.
• Application of analytical and numerical solutions to random and scale-free networks.
• Validation through theoretical analysis, simulations, and real network systems.

Main Results:

• A minimum proportion of reinforced inter-layer links is necessary to prevent abrupt network collapse.
• This minimum proportion acts as a boundary for different network phase transition types.
• The proposed inter-layer reinforcement strategy demonstrates superior efficiency compared to intra-layer reinforcement.
• The model is validated across various network types and real-world systems.

Conclusions:

• Reinforced inter-layer links are an effective strategy for enhancing the robustness of edge-coupled interdependent networks.
• The findings provide a theoretical basis for designing more resilient network infrastructures.
• This research offers a novel approach to mitigating cascading failures in complex systems.