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Small-world spectra in mean field theory
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Grabow, Carsten, Grosskinsky, Stefan and Timme, Marc (2012) Small-world spectra in mean field theory. Physical Review Letters, Vol.108 (No.21). Article no. 218701. doi:10.1103/PhysRevLett.108.218701
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Official URL: http://dx.doi.org/10.1103/PhysRevLett.108.218701
Abstract
Collective dynamics on small-world networks emerge in a broad range of systems with their spectra characterizing fundamental asymptotic features. Here we derive analytic mean field predictions for the spectra of small-world models that systematically interpolate between regular and random topologies by varying their randomness. These theoretical predictions agree well with the actual spectra (obtained by numerical diagonalization) for undirected and directed networks and from fully regular to strongly random topologies. These results may provide analytical insights to empirically found features of dynamics on small-world networks from various research fields, including biology, physics, engineering and social science.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Research Centres > Centre for Complexity Science Faculty of Science, Engineering and Medicine > Science > Mathematics |
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| Library of Congress Subject Headings (LCSH): | System analysis, Topology | ||||
| Journal or Publication Title: | Physical Review Letters | ||||
| Publisher: | American Physical Society | ||||
| ISSN: | 1079-7114 | ||||
| Official Date: | May 2012 | ||||
| Dates: |
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| Volume: | Vol.108 | ||||
| Number: | No.21 | ||||
| Number of Pages: | 5 | ||||
| Page Range: | Article no. 218701 | ||||
| DOI: | 10.1103/PhysRevLett.108.218701 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Funder: | Germany. Bundesministerium für Bildung und Forschung (BMBF), Universität Göttingen (GGNB), Max-Planck-Gesellschaft zur Förderung der Wissenschaften [Max Planck Society for the Advancement of Science], Engineering and Physical Sciences Research Council (EPSRC) | ||||
| Grant number: | 01GQ1005B (BMBF), GSC 226/1 (GGNB), EP/E501311/1 (EPSRC) | ||||
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