Sustaining a network by controlling a fraction of nodes

Abstract

Multi-stability is a widely observed phenomenon in real complex networked systems, such as technological infrastructures, ecological systems, gene regulation, transportation and more. Thus, even if the system is at equilibrium in a normal functional state, there might exist also a potential stable state having abnormal activity, into which the system might transition due to an external perturbation. Such a system can be regarded as unsustainable, due to the danger of falling into the potential undesired abnormal state. Here we explore, analytically and via simulations, how supporting the activity of a small fraction of nodes can turn an unsustainable system to become sustainable by eliminating the undesired potential stable state. We unveil a sustaining phase diagram in the presence of a fraction of controlled nodes. This phase diagram could provide how many controlled nodes are required for sustaining a given network as well as how strong the connectivity of the network should be for a given fraction of controllable nodes.