Dynamic interdependence and competition in multilayer networks

From critical infrastructure to physiology and the human brain, complex systems rarely occur in isolation. Instead, the functioning of nodes in one system often promotes or suppresses the functioning of nodes in another. Structural interdependence—that is, when the functionality of the nodes is determined exclusively by connectivity between layers—can be characterized via percolation processes on interdependent networks. However, modelling more general interactions between dynamical systems has remained an open problem. Here, we present a dynamic dependency framework that can capture interdependent and competitive interactions between dynamic systems, which we use to study synchronization and spreading processes in multilayer networks with interacting layers. By developing a mean-field theory, which we verify by simulations, we find coupled collective phenomena, including multistability, regions of coexistence, and macroscopic chaos. In interdependent dynamics, in particular, we observe hysteretic behaviours with abrupt (hybrid and explosive) transitions, that exhibit universal features that match those emerging from interdependent percolation. This dynamic dependency framework provides a powerful tool with which to improve our understanding of many of the interacting complex systems surrounding us.