Synchronizability of weighted aging scale-free networks
Yanli Zou1, Jie Zhu, Guanrong Chen
1Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China. zouyanli@sjtu.edu.cn
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 13, 2006
Summary
Synchronizability in weighted aging scale-free networks improves when older nodes dominate couplings. Conversely, younger node dominance weakens network synchronization, especially with heterogeneous in-degrees.
Area of Science:
- Complex networks
- Network synchronization
- Statistical physics
Background:
- Aging scale-free networks are crucial models for real-world systems.
- Understanding network synchronizability is key to controlling collective behavior.
- Non-normalized and asymmetrical coupling matrices present unique challenges.
Purpose of the Study:
- To investigate the synchronizability of weighted aging scale-free networks.
- To analyze the impact of coupling directionality (older-to-younger vs. younger-to-older nodes).
- To explore the effects of node degree heterogeneity and average degree on synchronization.
Main Methods:
- Theoretical analysis of network synchronizability.
- Mathematical modeling of weighted aging scale-free networks.
- Numerical simulations using coupled Lorenz systems for verification.
Main Results:
- Synchronizability is enhanced when older nodes dominate couplings, particularly with heterogeneous out-degrees and homogeneous in-degrees.
- Synchronizability is significantly weakened or lost when younger nodes dominate couplings, especially with homogeneous out-degrees and heterogeneous in-degrees.
- Node heterogeneity and smaller average degrees can improve synchronizability under specific weighting parameter values.
Conclusions:
- Coupling directionality plays a critical role in the synchronizability of weighted aging scale-free networks.
- Network topology, specifically degree heterogeneity and average degree, influences synchronization dynamics.
- The findings provide insights into designing and controlling synchronization in complex systems.
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