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arXiv · 1704.01349

Indirect Long-range Interactions and Network Synchronization

Ernesto Estrada·Lucia Valentina Gambuzza·Mattia Frasca
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Abstract

The dynamical behavior of networked complex systems is shaped not only by the direct links among the units, but also by the long-range interactions occurring through the many existing paths connecting the network nodes. In this work, we study how synchronization dynamics is influenced by these long-range interactions, formulating a model of coupled oscillators that incorporates this type of interactions through the use of $d-$path Laplacian matrices. We study synchronizability of these networks by the analysis of the Laplacian spectra, both theoretically and numerically, for real-world networks and artificial models. Our analysis reveal that in all networks long-range interactions improve network synchronizability with an impact that depends on the original structure, for instance it is greater for graphs having a larger diameter. We also investigate the effects of edge removal in graphs with long-range interactions and, as a major result, find that the removal process becomes more critical, since also the long-range influence of the removed link disappears.

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Ernesto Estrada, Lucia Valentina Gambuzza, Mattia Frasca. 2017-04-05. Indirect Long-range Interactions and Network Synchronization. https://arxiv.org/abs/1704.01349

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