Figure 3: Energy scaling as time horizon and input node fraction are varied.
From: Energy scaling of targeted optimal control of complex networks
Besides the average degree and power-law exponent that describe the underlying graph of the network (Fig. 2), there are other parameters that can affect the control energy such as the time horizon and the number of designated input nodes. (a) The time horizon, defined as tf−t0, is varied for networks constructed using the static model with the following properties: n=500; γin=γout=3.0; kav=5.0; and nd=0.5. As we choose t0=0, the time horizon is equivalent to just tf. The main plot shows how the log of the maximum control energy changes with target node fraction, p/n. Each point represents the mean over 50 realizations, and error bars represent one s.d. The inset shows how η changes with the time horizon. We see a sharp increase as the time horizon decreases. (b) We also investigate how η varies with the number of input nodes. The same class of network is examined as in a: n=500; γin=γout=3.0; and kav=5.0. For both simulations, nodes are randomly and independently chosen to be in each target set. We see that η grows as the number of input nodes decreases as shown in the inset.
