Figure 6: Average energy for increasing state weight matrices.
From: Energy scaling of targeted optimal control of complex networks
We demonstrate that for both model networks and real data sets, increasing ζ (where the state weight matrix, Q=ζIn), does not significantly increase the average energy. (a) The static model is used to generate model networks with parameters n=300 and kav=5.0, where nd=0.5. Note that the order of magnitude, here represented as a linear scale with respect to the logarithm of the energy, is approximately constant. Each point is averaged over 50 iterations of model networks and final desired states, which have Euclidean norm equal to one. (b) Two real networks are also examined and the average energy is computed. Each point is the mean over 50 realizations where each realization represents a choice of final condition such that the final condition has Euclidean norm equal to one. For both studies, error bars represent one s.d.
