Universality in network dynamics
- PMID: 24319492
- PMCID: PMC3852675
- DOI: 10.1038/nphys2741
Universality in network dynamics
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.
Figures



































References
-
- Caldarelli G. Scale-free networks: complex webs in nature and technology. Oxfrod University Press; New York: 2007.
-
- Drogovtsev SN, Mendez JFF. Evolution of networks: from biological nets to the Internet and WWW. Oxford University Press; Oxford: 2003.
-
- Strogatz SH. Exploring complex networks. Nature. 2001;410:268–276. - PubMed
-
- Helbing D, Jost J, Kantz H, editors. Networks and Heterogeneous Media (NHM) Vol. 3. AIMS; Springfield, MO., USA: 2008. Networks and complexity; pp. 185–411.
-
- Newman MEJ. Networks - an introduction. Oxford University Press; New York: 2010.
Grants and funding
LinkOut - more resources
Full Text Sources
Other Literature Sources