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Broad lifetime distributions for ordering dynamics in complex networks.

R Toivonen¹, X Castelló, V M Eguíluz

¹Department of Biomedical Engineering and Computational Science (BECS), Helsinki University of Technology, FIN-02015 HUT, Finland. Riita.Toivonen@tkk.fi

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|March 5, 2009

Summary

This summary is machine-generated.

A characteristic time scale for ordering dynamics in complex networks does not exist when there is significant mesoscale heterogeneity. This heterogeneity creates long-lasting dynamical metastable states, impacting network behavior.

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Area of Science:

Complex Systems Science
Network Science
Statistical Physics

Background:

Ordering dynamics in finite complex networks often exhibit characteristic time scales.
Understanding the conditions for the absence of such time scales is crucial for predicting network behavior.

Purpose of the Study:

To identify conditions leading to the absence of a characteristic time scale for ordering dynamics in complex networks.
To investigate the role of network structure, specifically mesoscale heterogeneity, in this phenomenon.

Main Methods:

Studied random networks and networks with community structure (clique-based).
Analyzed ordering dynamics towards two absorbing states.
Investigated the impact of mesoscale heterogeneity on dynamical properties.

Main Results:

Large heterogeneity at the mesoscale level is a sufficient mechanism for the absence of a characteristic time scale.
This heterogeneity leads to the emergence of dynamical metastable states.
These metastable states persist across all time scales.

Conclusions:

Mesoscale heterogeneity in complex networks can eliminate characteristic time scales for ordering dynamics.
Dynamical metastable states are a key feature resulting from such heterogeneity.
Findings have implications for understanding system stability and long-term behavior in heterogeneous networks.