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Hybrid phase transition into an absorbing state: Percolation and avalanches.
Deokjae Lee1, S Choi1, M Stippinger2
1CCSS, CTP and Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea.
Physical Review. E
|May 14, 2016
Summary
Interdependent networks collapse due to cascading failures, exhibiting a hybrid phase transition (HPT). This study reveals critical behaviors like diverging fluctuations and power-law avalanche sizes in these complex networks.
Area of Science:
- Complex systems
- Network science
- Statistical physics
Background:
- Interdependent networks are susceptible to cascading failures, leading to fragility.
- Hybrid phase transitions (HPT) characterize the sudden collapse of these networks.
- Understanding critical phenomena in HPT is crucial for network resilience.
Purpose of the Study:
- To investigate the critical behaviors of hybrid percolation transitions in Erdős-Rényi and 2D interdependent networks.
- To analyze the relationship between order parameter fluctuations and avalanche size distributions.
- To characterize the exponents governing HPT and their scaling laws.
Main Methods:
- Analysis of Erdős-Rényi and two-dimensional interdependent network models.
- Study of percolation transitions and cascading failures.
- Characterization of order parameter fluctuations and avalanche statistics.
Main Results:
- Hybrid percolation transitions exhibit two critical behaviors: diverging order parameter fluctuations and power-law avalanche size distributions.
- Global avalanches occur at the transition point, while finite avalanches follow a power-law distribution, indicating HPT in avalanche statistics.
- The order parameter exponent βm is generally 1/2, and a scaling law 1-βm=γa connects critical behaviors.
Conclusions:
- Interdependent networks display complex critical phenomena during hybrid phase transitions.
- Avalanche statistics in these networks also exhibit hybrid phase transition characteristics.
- The identified scaling law provides a deeper understanding of the interconnected critical behaviors in complex networks.
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