Collective fluctuations in networks of noisy components

Naoki Masuda, Yoji Kawamura, Hiroshi Kori*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


Collective dynamics result from interactions among noisy dynamical components. Examples include heartbeats, circadian rhythms and various pattern formations. Because of noise in each component, collective dynamics inevitably involve fluctuations, which may crucially affect the functioning of the system. However, the relation between the fluctuations in isolated individual components and those in collective dynamics is not clear. Here, we study a linear dynamical system of networked components subjected to independent Gaussian noise and analytically show that the connectivity of networks determines the intensity of fluctuations in the collective dynamics. Remarkably, in general directed networks including scale-free networks, the fluctuations decrease more slowly with system size than the standard law stated by the central limit theorem. They even remain finite for a large system size when global directionality of the network exists. Moreover, such non-trivial behavior appears even in undirected networks when nonlinear dynamical systems are considered. We demonstrate it with a coupled oscillator system.

Original languageEnglish
Article number093007
JournalNew Journal of Physics
Publication statusPublished - 2010 Sept 6
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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