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Multilayer NetworksStructure and Function$
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Ginestra Bianconi

Print publication date: 2018

Print ISBN-13: 9780198753919

Published to Oxford Scholarship Online: July 2018

DOI: 10.1093/oso/9780198753919.001.0001

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Synchronization, Non-linear Dynamics and Control

Synchronization, Non-linear Dynamics and Control

(p.324) 15 Synchronization, Non-linear Dynamics and Control
Multilayer Networks

Ginestra Bianconi

Oxford University Press

This chapter is entirely devoted to characterizing non-linear dynamics on multilayer networks. Special attention is given to recent results on the stability of synchronization that extend the Master Stability Function approach to the multilayer networks scenario. Discontinous synchronization transitions on multiplex networks recently reported in the literature are also discussed, and their application discussed in the context of brain networks. This chapter also presents an overview of the major results regarding pattern formation in multilayer networks, and the proposed characterization of multivariate time series using multiplex visibility graphs. Finally, the chapter discusses several approaches for multiplex network control where the dynamical state of a multiplex network needs to be controlled by eternal signals placed on replica nodes satisfying some structural constraints.

Keywords:   non-linear dynamics, synchronization, Master Stability Function, discontinuous synchronization transition, pattern formation, multivariate time series, multilayer network control

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