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Rare-region effects in the contact process on networks
Róbert Juhász1, Géza Ódor, Claudio Castellano
1Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, H-1525 Budapest, P.O. Box 49, Hungary.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
Summary
This study reveals that intrinsic node disorder and network structure can cause slow down propagation phenomena, leading to Griffiths phases and rare-region effects on complex networks.
Area of Science:
- Complex systems science
- Network science
- Statistical physics
Background:
- Networks are fundamental to understanding complex systems and dynamical processes.
- Quenched disorder, both in nodes and topology, presents a significant challenge in network dynamics.
- The contact process is a key model for studying propagation phenomena.
Purpose of the Study:
- To analyze the contact process with node-dependent infection rates (intrinsic quenched disorder) on complex networks.
- To investigate the emergence of Griffiths phases and rare-region effects due to disorder and network topology.
- To explore implications for propagation phenomena and dynamical processes on networks.
Main Methods:
- Analysis of the contact process on Erdős-Rényi networks with intrinsic quenched disorder.
- Investigation of propagation dynamics on complex networks with topological heterogeneity.
- Modeling Griffiths phases and rare-region effects in generalized small-world networks.
Main Results:
- Griffiths phases and anomalously slow relaxation (algebraic, logarithmic) observed on Erdős-Rényi networks due to intrinsic quenched disorder.
- Prediction of similar effects on other network topologies with a nonvanishing percolation threshold.
- Emergence of Griffiths phases even with constant epidemic rates due to topological heterogeneity in finite-dimensional networks, such as generalized small-world networks.
Conclusions:
- Intrinsic node disorder and topological heterogeneity significantly impact propagation dynamics on complex networks.
- Griffiths phases and rare-region effects lead to anomalously slow relaxation, affecting various dynamical processes.
- Findings are relevant for both theoretical models and empirical analysis of network phenomena.
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