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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 9: Statistics and Dynamics of/on Networks (joint session BP/DY/SOE)

SOE 9.3: Talk

Tuesday, March 12, 2013, 10:00–10:15, H47

Small-World Network Spectra in Mean-Field Theory — •Carsten Grabow¹, Stefan Grosskinsky², and Marc Timme³ — ¹Potsdam Institute for Climate Impact Research, Potsdam, Germany — ²Mathematics Institute and Centre for Complexity Science, Warwick, UK — ³Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany

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. (Based on Grabow, C., Grosskinsky, S. & Timme, M. Small-World Network Spectra in Mean-Field Theory. Phys. Rev. Lett 108, (2012).)