Appropriate time to apply control input to complex dynamical systems

Abstract Controlling a network structure has many potential applications many fields. In order to have an effective network control, not only finding good driver nodes is important, but also finding the optimal time to apply the external control signals to network nodes has a critical role. If applied in an appropriate time, one might be to control a network with a smaller control signals, and thus less energy. In this manuscript, we show that there is a relationship between the strength of the internal fluxes and the effectiveness of the external control signal. To be more effective, external control signals should be applied when the strength of the internal states is the smallest. We validate this claim on synthetic networks as well as a number of real networks. Our results may have important implications in systems medicine, in order to find the most appropriate time to inject drugs as a signal to control diseases.