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Discrete surface growth process as a synchronization mechanism for scale-free complex networks
A L Pastore y Piontti1, P A Macri, L A Braunstein
1Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, 7600 Mar del Plata, Argentina.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2007
Summary
The discrete surface growth model synchronizes networks better than the Edward-Wilkinson process, especially on scale-free networks. The discrete model avoids nonphysical synchronization issues seen in the EW process for certain network types.
Area of Science:
- Complex Systems
- Network Science
- Statistical Physics
Background:
- Scale-free networks exhibit a degree distribution P(k) ~ k{-lambda}.
- Surface growth models are used to study synchronization phenomena.
- The Edward-Wilkinson (EW) process is a standard model for surface growth.
Purpose of the Study:
- To investigate the discrete surface growth process with relaxation to the minimum as a synchronization mechanism on scale-free networks.
- To compare its performance with the Edward-Wilkinson process on these networks.
- To identify limitations of the EW process in scale-free network synchronization.
Main Methods:
- Analysis of the discrete surface growth process on scale-free networks.
- Comparison with the Edward-Wilkinson process on the same network types.
- Examination of roughness scaling behavior and synchronization properties.
Main Results:
- For scale-free networks with lambda<3, the EW process fails to explain saturation roughness scaling.
- The EW process exhibits nonphysical spontaneous synchronization enhancement with increasing system size on these networks, due to finite size effects.
- The discrete surface growth process provides a valid synchronization mechanism for all lambda values on scale-free networks without these flaws.
Conclusions:
- The discrete surface growth process is a more robust synchronization mechanism for scale-free networks compared to the EW process, particularly for lambda<3.
- The EW process's limitations on scale-free networks stem from finite size effects, leading to unrealistic synchronization behavior.
- The discrete surface growth model offers a universally applicable approach for synchronization studies on diverse network structures.
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