Figure 2: Relationship between edge control strength and minimal control time.
From: A geometrical approach to control and controllability of nonlinear dynamical networks
For the T-cell network, (a) an inverted rectangular control signal of duration 
and amplitude 
, where μ0 is the original parameter value and μn is the control parameter value. A saddle-node bifurcation occurs for μ=μc, so Δe=μc−μn is the excessive amount of the parameter change over the critical value μc. (b,c) Minimal control time 
versus μn, where parameter control is applied to the activation edge from node ‘S1P’ to node ‘PDGFR’ and to the inhibitory edge from ‘DISC’ to ‘MCL1’, respectively. These four nodes are indicated with the solid black circles in Fig. 1a. The corresponding plots on a logarithmic scale in the insets of (b,c) suggest a power-law scaling behaviour between 
and Δe (equation (2)). The fitted power-law scaling exponents are β≈−0.44 and −0.55, respectively, for (b,c).
