  Percolation establishes the connectivity of complex networks and is one of
the most fundamental critical phenomena for the study of complex systems. On
simple networks, percolation displays a second-order phase transition; on
multiplex networks, the percolation transition can become discontinuous.
However, little is known about percolation in networks with higher-order
interactions. Here, we show that percolation can be turned into a fully-fledged
dynamical process when higher-order interactions are taken into account. By
introducing signed triadic interactions, in which a node can regulate the
interactions between two other nodes, we define triadic percolation. We uncover
that in this paradigmatic model the connectivity of the network changes in time
and that the order parameter undergoes a period-doubling and a route to chaos.
We provide a general theory for triadic percolation which accurately predicts
the full phase diagram on random graphs as confirmed by extensive numerical
simulations. We find that triadic percolation on real network topologies
reveals a similar phenomenology. These results radically change our
understanding of percolation and may be used to study complex systems in which
the functional connectivity is changing in time dynamically and in a
non-trivial way, such as in neural and climate networks.
