Critical behavior of a two-step contagion model with multiple seeds
Wonjun Choi1, Deokjae Lee1, B Kahng1
1CCSS, CTP, and Department of Physics and Astronomy, Seoul National University, Seoul 08826, Republic of Korea.
Physical Review. E
|July 16, 2017
Summary
This study reveals how contagion dynamics differ with single versus multiple seeds in percolation models. Multiple seeds can merge clusters, leading to hybrid or continuous transitions unlike single-seed models.
Area of Science:
- Complex Systems
- Network Science
- Epidemiology
Background:
- Percolation transitions are fundamental to understanding network phenomena.
- Cascade dynamics and contagion spread are key mechanisms in complex systems.
- Discontinuous transitions in contagion models require further mechanistic understanding.
Purpose of the Study:
- To investigate the impact of multiple seeds on contagion spread and percolation transitions.
- To analyze the transition behaviors (hybrid, continuous) in a two-step contagion model.
- To determine critical exponents for different seeding scenarios.
Main Methods:
- Analytical modeling of a two-step contagion process.
- Numerical simulations to observe cluster dynamics and transitions.
- Characterization of critical exponents for hybrid and continuous transitions.
Main Results:
- Single-seed contagion leads to non-merging cluster growth.
- Multiple seeds (O(N)) induce cluster merging, mimicking percolation.
- Hybrid transitions (continuous and discontinuous) observed with low seed density.
- Continuous transitions observed with high seed density.
Conclusions:
- The number of initial seeds significantly alters contagion spread and transition dynamics.
- Multiple seeds introduce cluster merging, leading to distinct critical behaviors compared to single-seed models.
- The study provides a comprehensive analysis of critical exponents for hybrid and continuous transitions in this model.
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