Dynamical leaps due to microscopic changes in multiplex networks

Marina Diakonova1,2, José J. Ramasco2 and Víctor M. Eguíluz2

1School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom.
2Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), 07122 Palma de Mallorca, Spain.

(April 2016)

Recent developments of the multiplex paradigm included efforts to understand the role played by the presence of several layers on the dynamics of processes running on these networks. The possible existence of new phenomena associated to the richer topology has been discussed and examples of these differences have been systematically searched. Here, we show that the interconnectivity of the layers may have an important impact on the speed of the dynamics run in the network and that microscopic changes such as the addition of one single inter-layer link can notably affect the arrival at a global stationary state. As a practical verification, these results obtained with spectral techniques are confirmed with a Kuramoto dynamics for which the synchronization consistently delays after the addition of single inter-layer links.