Por Gareth Baxter (Departamento de Física e I3N, Universidade de Aveiro, Portugal).

Networks are an effective way to represent the heterogeneous interactions in many complex systems. Percolation on networks reveals not only structural properties of the network, but also helps to understand processes occurring on networks, such as epidemic spreading.

Systems with multiple sub-systems or with multiple types of connections may be represented as multi-layer or multiplex networks. I will discuss the two main ways to generalise percolation to multi-layer networks, and the relationship between them. These percolation rules lead to novel critical phenomena, such as a discontinuous hybrid phase transition, associated with cascading avalanches of failures. I will discuss recent theoretical results in this area.