Talk:Pinning control
Reviewer 1
This is a very timely and well done article: bravo Mario! Said that, I would very much appreciate if you could address the following comments: 1. Please delete "When all the nodes converge towards a point in the state space, then we say that the network achieves consensus." I would indeed say that consensus is often used interchangeably with synchronization even if the state if changing in time. If you do not agree, at least please add a comment acknowledging that sometimes authors would use the word consensus beyond fixed point synchronization; 2. In equation (5), I believe x should be replaced by y; 3. Please fix the subscript of $\delta_{11}$ in the definition of $\mathcal{M}$; 4. As an intermediate step between static and adaptive pinning, I would also mention my work on node-to-node pinning control in Chaos 2009, Chaos 2013, and Physica D 2010, which address the case of pinning a network by randomly or periodically varying the pinning site; 5. Maybe it would be a good idea to comment on the analogies between pinning control and leader-follower consensus; 6. I would add a brief comment on the MSF to highlight its working assumptions and the fact that it applies to local stability of the synchronization manifold, which is set by the pinner dynamics; and 7. Please define $\alpha$
Reviewer 2
Minor Comments (The following comments are given through reading, so are itemized in reading order)
“characterize” should be “characterizing”
The defining formula of synchronization: it is better to use Euclidean norm, otherwise the interactions between the two state vectors x_i and x_j is restricted to be component-wise, as it stands now. Using a norm, inter-component interactions are allowed through the synchronizing process. Same suggestion for the pinning control formula thereafter.
“trajectory/point”: since “point” is also a special trajectory, it may be deleted.
“Master Stability Function (MSF) approach”: please give one key reference about this concept.
“vertex”: please unify the name “node” and “vertex”, and also “edge” and “link”, in the same article.
The matrix below Eq (5) should be M rather than M_{ij}
Paper by Chen, Liu and Lu (2007) studies “local” but not “global” pinning control, where eigan-analysis was used.
“makes pinning controllability not feasible with a static approach” is not clear what it means by “not feasible”. Perhaps the sentence can be slightly modified by adding a few more words, e.g., “makes pinning controllability not feasible with a static approach, for example with parameter uncertainties”
Two terms, q_i and e_i, in Eq (6) need to be defined.
“the coupling gains \sigma_i defines”: “gains” should be “gain”
\eta_i in Eq (7) needs to be defined.
“according to the edge-snapping mechanism” - - > either “according to the above edge-snapping mechanism” or “according to the edge-snapping mechanism (8)”, so as to make clear what “edge-snapping mechanism” means.
“communications delays”: using “communication delays” is better
In “highly dependent on the initial state”: “state” - - > “states”
In sentence “where the weight \apha_{ij} is associated to every undirected edge of the target pinning edge”: there are two confusions here: (1) how can one weight be assigned to “every” edge? (2) how can one “target pinning edge” have “every undirected edge”?
Coefficients \nu and c in Eq (11) need to be defined.
Coefficients in (12)-(13) need to be defined (they take some specific values for the circuit to be chaotic).
“only one node is directly pinned”; the word “directly” is confusing, which may be removed.
“Moreover, \sigma_{ij}(0) with (i,j) \in \epsilon and q_i(0)”: these notations need to be defined or referred back to their first definitions.
