Taming out-of-equilibrium dynamics on interconnected networks

A wide variety of social, biological or technological systems can be described as processes taking place on networked structures in continuous interaction with other networks. We propose here a new methodology to describe, anticipate and manage, in real time, the out-of-equilibrium dynamics of processes that evolve on interconnected networks. This goal is achieved through the full analytical treatment of the phenomenology and its reduction to a two-dimensional flux diagram, allowing us to predict at every time step the dynamical consequences of modifying the links between the different ensembles. Our results are consistent with real data and the methodology can be translated to clustered networks and/or interconnected networks of any size, topology or origin, from the struggle for knowledge on innovation structures to international economic relations or disease spreading on social groups.We acknowledge the assistance of D. Peralta-Salas in the analytical computations, fruitful conversations with P. Catalán, J.A. Cuesta, F.M. Dopico, S. Manrubia, A.-L. Sanz and P. Yubero, and the support of the Spanish Ministerio de Economía y Competitividad under projects FIS2014-57686-P (ViralESS), CSO2016-74888-C4-4-R (CITiTALENT), FIS2017-89773-P (MiMevo) and FIS2017-84151-P. J.A. is supported through grant SEV-2013-0347