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History-dependent percolation on multiplex networks
Ming Li1, Linyuan Lü2, Youjin Deng3
1Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei 230026, China.
National Science Review
|October 25, 2021
Summary
This study introduces a unified framework for understanding percolation transitions in interacting networks. The research reveals how system history influences transitions, with significant changes observed at infinite generations, offering insights into network structures.
Area of Science:
- Complex systems science
- Network science
- Statistical physics
Background:
- Interconnected systems and dynamics are widely studied across disciplines.
- Existing models often lack a comprehensive understanding of connections between different percolation transitions.
- Percolation theory is crucial for understanding network behavior and phase transitions.
Purpose of the Study:
- To propose a unified framework for analyzing discontinuous percolation transitions in interacting networks.
- To investigate the history-dependent nature of percolation processes.
- To explore the impact of generations on transition dynamics.
Main Methods:
- Development of a novel, history-dependent percolation model.
- Theoretical analysis of the model's behavior across generations.
- Monte Carlo simulations to validate theoretical findings.
Main Results:
- The percolation transition nature is consistent at finite generations.
- An abrupt change in transition behavior is observed at infinite generations.
- The model demonstrates applicability to real-world network analysis.
Conclusions:
- The proposed framework unifies the study of percolation transitions in interacting networks.
- System history significantly impacts percolation dynamics, especially in the long-term (infinite generations).
- The model offers a general method for network structure exploration and applications like detecting abnormalities in human brain networks.
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