Universality in network dynamics

Baruch Barzel, Albert László Barabási

Research output: Contribution to journalArticlepeer-review

236 Scopus citations

Abstract

Despite significant advances in characterizing the structural properties of complex networks, a mathematical framework that uncovers the universal properties of the interplay between the topology and the dynamics of complex systems continues to elude us. Here we develop a self-consistent theory of dynamical perturbations in complex systems, allowing us to systematically separate the contribution of the network topology and dynamics. The formalism covers a broad range of steady-state dynamical processes and offers testable predictions regarding the system's response to perturbations and the development of correlations. It predicts several distinct universality classes whose characteristics can be derived directly from the continuum equation governing the system's dynamics and which are validated on several canonical network-based dynamical systems, from biochemical dynamics to epidemic spreading. Finally, we collect experimental data pertaining to social and biological systems, demonstrating that we can accurately uncover their universality class even in the absence of an appropriate continuum theory that governs the system's dynamics.

Original languageEnglish
Pages (from-to)673-681
Number of pages9
JournalNature Physics
Volume9
Issue number10
DOIs
StatePublished - Oct 2013
Externally publishedYes

Bibliographical note

Funding Information:
We thank A. Vespignani, A. Sharma, F. Simini, J. Menche, S. Rabello, G. Ghoshal, Y-Y Liu, T. Jia, M. Pósfai, C. Song, Y-Y. Ahn, N. Blumm, D. Wang, Z. Qu, M. Schich, D. Ghiassian, S. Gil, P. Hövel, J. Gao, M. Kitsak, M. Martino, R. Sinatra, G. Tsekenis, L. Chi, B. Gabriel, Q. Jin and Y. Li for discussions, and S. S. Aleva, S. Weiss, J. de Nicolo and A. Pawling for their support. This work was supported by DARPA Grant Number 11645021ő The DARPA Social Media in Strategic Communications project under agreement number W911NF-12-C-0028ő the Network Science Collaborative Technology Alliance sponsored by the US Army Research Laboratory under Agreement Number W911NF-09-02-0053ő the Office of Naval Research under Agreement Number N000141010968 and the Defense Threat Reduction Agency awards WMD BRBAA07-J-2-0035 and BRBAA08-Per4-C-2-0033ő the National Institute of Health, Center of Excellence of Genomic Science (CEGS), Grant number NIH CEGS 1P50HG4233ő and the National Institute of Health, Award number 1U01HL108630-01.

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