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Critical behavior of efficiency dynamics in small-world networks
Sheng-You Huang1, Xian-Wu Zou, Zhi-Jie Tan
1Department of Physics, Wuhan University, Wuhan 430072, People's Republic of China.
Summary
This study reveals that efficiency dynamics in small-world networks exhibit a critical transition at a specific disorder level (phi(c) > 0). This transition arises from both network structure and the model's dynamics, offering insights into complex system behaviors.
Area of Science:
- Complex Systems
- Network Science
- Computational Social Science
Background:
- Dynamical processes in small-world networks often display critical transitions.
- Geometrical properties typically show critical behavior at zero disorder (phi(c)=0).
- The reasons for transitions occurring at non-zero disorder (phi(c)>0) remain unclear.
Purpose of the Study:
- To investigate the underlying mechanisms of critical transitions at non-zero disorder in small-world networks.
- To present a social model of efficiency dynamics exhibiting a transition at phi(c)>0.
- To determine the critical point and contributing factors for this transition.
Main Methods:
- Development of a simple social model for efficiency dynamics.
- Analysis of small-world network properties.
- Finite-size analysis to determine the critical point.
Main Results:
- The social model demonstrates a critical transition at a finite disorder, phi(c) > 0.
- The critical point was estimated to be approximately phi(c) ≈ 0.098.
- Both network geometrical properties and model-specific dynamics were found to influence the transition.
Conclusions:
- The critical transition at phi(c)>0 in this model is a result of interplay between network structure and dynamics.
- This finding contributes to understanding critical phenomena in various dynamical processes on small-world networks.
- The study highlights the importance of considering both structural and dynamical aspects for analyzing network transitions.