Dresden 2014 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 24: Networks - Statistics and Dynamics (joint session DY/ BP/ SOE)
DY 24.7: Talk
Wednesday, April 2, 2014, 16:30–16:45, ZEU 118
Temporal networks: Laplacian spectra and synchronization — •Konstantin Klemm1,2, Naoki Masuda3, and Victor M. Eguiluz4 — 1Bioinformatics, Institute of Computer Science, Leipzig University, Germany — 2Bioinformatics and Computational Biology, University of Vienna, Austria — 3Department of Mathematical Informatics, The University of Tokyo, Japan — 4Instituto de Fisica Interdisciplinar y Sistemas Complejos, Palma de Mallorca, Spain
Interactions among units in complex systems occur in a specific sequential order thus affecting the flow of information, the propagation of diseases, and general dynamical processes. We investigate the Laplacian spectrum of temporal networks and compare it with that of the corresponding aggregate network. First, we show that the spectrum of the ensemble average of a temporal network has identical eigenmodes but smaller eigenvalues than the aggregate networks. In large networks without edge condensation, the expected temporal dynamics is a time-rescaled version of the aggregate dynamics. Even for single sequential realizations, diffusive dynamics is slower in temporal networks [1]. These discrepancies are due to the noncommutability of interactions. The final part of the presentation uses the calculated spectra to predict the stability of non linear-systems with diffusive temporal couplings.
[1] N. Masuda, K. Klemm, V. M. Eguiluz, Phys. Rev. Lett. 111, 188701 (2013).