Critical Phenomena in Multilayer Networks

Network science has provided a set of powerful theoretical results for the description of critical phenomena in complex systems. These represent fundamental tools for the design and control of real networked systems with concrete and practical applications. Many of these results have been, however, formulated in the framework of independent networks, i.e., closed systems that do not interact with nor depend on other networks. This is a weak hypothesis because in the realworld networks cannot be considered as independent entities. For instance, critical infrastructure are very often and intentionally coupled together: the functioning of the networks of water and food supply, communications, fuel, financial transactions and power generation and transmission depend one on the other. For this reason, many of the classical results of network science have been questioned, and recent research has provided evidence that many of the results valid for isolated networks are indeed not verified for interacting (or so called multilayer) networked systems. With this thesis we present new results in the field of both linear and nonlinear dynamical processes in the context of multilayer networks, namely diffusion and percolation. While diffusion is naturally related to the concept of walks and navigability of a network, percolation addresses the concept of stability and resilience of a network under random and targeted attacks.