  The recent paper by W.-X. Wang, Y.-C. Lai, J. Ren, B. Li & C. Grebogi
[arXiv:1107.2177v1] proposed a method for the control of complex networks with
nonlinear dynamics based on linearizing the system around a finite number of
local desired states. The authors purport that any bidirectional network with
one-dimensional intrinsic node dynamics can be fully controlled by a single
driver node, which can be any node in the network, regardless of the network
topology. According to this result, a network with an arbitrarily large number
of nodes (a million, a billion, or even more) could be controlled by a single
node. Here we show, however, that this result is specious and that it does not
hold true even for networks with only two nodes. We demonstrate that the
erroneous results are a consequence of a fundamental flaw in the proposed
method, namely, that reaching a local desired state using the proposed
linearization procedure generally requires a nonlocal trajectory, which grossly
violates the linear approximation. Their further conclusion that network
systems with nonlinear dynamics are more controllable than those with linear
dynamics is a known fact presented as novel based on a flawed argument. A
central problem underlying the authors' argument is that their formulation is
entirely based on the number of driver nodes required to reach a desired
state---even when this number is one, keeping the system at that desired state
generally requires directly controlling all nodes in the network. When this is
taken into account, the conclusion that nonlinear dynamics can facilitate
network control was already anticipated in S.P. Cornelius, W.L. Kath & A.E.
Motter [arXiv:1105.3726v1], which is not referenced in their paper. If one
insists on using the authors' formulation, then, in contradiction to their
claim, nonlinear systems would never be more controllable than linear ones
because...
