Intrinsic dynamics induce global symmetry in network controllability

Scientific Reports

Volumn 5, Issue , 2015, Pages 8422-

  Zhao, Chen ^a   Wang, Wen Xu ^a   Liu, Yang Yu ^b,c   Slotine, Jean Jacques ^d,e  

^a BEIJING NORMAL UNIVERSITY   (China)

^b HARVARD MEDICAL SCHOOL   (United States)

^c NORTHEASTERN UNIVERSITY   (United States)

^d MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^e Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84922991845     PISSN: None     EISSN: 20452322     Source Type: Journal    
DOI: 10.1038/srep08422     Document Type: Article

References (34)

1. Strogatz, S. H. Exploring complex networks. Nature 410, 268-276 (2001).
2. Albert, R. & Barabasi, A.-L. Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47-97 (2002).
3. Watts, D. J. & Strogatz, S. H. Collective dynamics of 'small-world' networks. Nature 393, 440-442 (1998).
4. Barabá si, A.-L. & Albert, R. Emergence of scaling in random networks. Science 286, 509-512 (1999).
5. Liu, Y.-Y., Slotine, J.-J. & Barabá si, A.-L. Controllability of complex networks. Nature 473, 167-173 (2011).
6. Nepusz, T. & Vicsek, T. Controlling edge dynamics in complex networks. Nat. Phys. 8, 568-573 (2012).
7. Cornelius, S. P., Kath, W. L.&Motter, A. E. Realistic control of network dynamics. Nat. commun. 4, 1942 (2013).
8. Ruths, J. & Ruths, D. Control Profiles of Complex Networks. Science 343, 1373-1376 (2014).
9. Kalman, R. E.Mathematical description of linear dynamical systems. J. Soc. Indus. Appl. Math. Ser. A 1, 152-192 (1963).
10. Luenberger, D. G. Introduction to Dynamic Systems: Theory, Models, & Applications (John Wiley & Sons, New York, 1979).
11. Lin, C. T. Structural controllability. IEEE Trans. Autom. Control 19, 201-208 (1974).
12. Shields, R. W. & Pearson, J. B. Structural controllability of multiinput linear systems. IEEE Trans. Autom. Control 21, 203-212 (1976).
13. Hosoe, S. Determination of generic dimensions of controllable subspaces and its application. IEEE Trans. Autom. Control 25, 11921196 (1980).
14. Commault, C., Dion, J.-M. & van der Woude, J. W. Characterization of generic properties of linear structured systems for efficient computations. Kybernetika 38, 503-520 (2002).
15. Dion, J.-M., Commault, C. & van der Woude, J. Generic properties and control of linear structured systems: a survey. Automatica 39, 1125 (2003).
16. Liu, Y.-Y., Slotine, J.-J. & Barabá si, A.-L. Control centrality and hierarchical structure in complex networks. PLoS ONE 7, e44459 (2012).
17. Wang, W.-X., Ni, X., Lai, Y.-C. & Grebogi, C. Optimizing controllability of complex networks by minimum structural perturbations. Phys. Rev. E 85, 026115 (2012).
18. Tang, Y., Gao, H., Zou, W. & Kurths, J. Identifying controlling nodes in neuronal networks in different scales. PLoS ONE 7, e41375 (2012).
19. Wang, B., Gao, L. & Gao, Y. Control range: a controllability-based index for node significance in directed networks. J. Stat. Mech.: Theor. Exp. 2012, P04011 (2012).
20. Pó sfai, M., Liu, Y.-Y., Slotine, J.-J. & Barabá si, A.-L. Effect of correlations on network controllability. Sci. Rep. 3, 1067 (2013).
21. Jia, T., Liu, Y.-Y., Csó ka, E., Pó sfai, M., Slotine, J.-J.&Barabá si, A.-L. Emergence of bimodality in controlling complex networks. Nat. Commun. 4, 2002 (2013).
22. Yan, G., Ren, J., Lai, Y.-C., Lai, C.-H. & Li, B. Controlling complex networks: how much energy is needed? Phys. Rev. Lett. 108, 218703 (2012).
23. Gutiérez, R., Sendiña-Nadal, I., Zanin, M., Papo, D. & Boccaletti, S. Targeting the dynamics of complex networks. Sci. Rep. 2, 396 (2012).
24. Liu, Y.-Y., Slotine, J.-J. & Barabási, A.-L. Observability of complex systems. Proc. Natl. Acad. Sci. USA 110, 2460-2465 (2013).
25. Sun, J. & Motter, A. E. Controllability transition and nonlocality in network control. Phys. Rev. Lett. 110, 208701 (2013).
26. Cowan, N. J., Chastain, E. J., Vilhena, D. A., Freudenberg, J. S. & Bergstrom, C. T. Nodal dynamics, not degree distributions, determine the structural controllability of complex networks. PLoS ONE 7, e38398 (2012).
27. Yuan, Z., Zhao, C., Di, Z., Wang, W.-X. & Lai, Y.-C. Exact controllability of complex networks. Nat. Commun. 4, 2447 (2013).
28. Sontag, E. D. Mathematical Control Theory: Deterministic Finite Dimensional Systems (Springer, New York, 1998).
29. Antsaklis, P. J. & Michel, A. N. Linear Systems (McGraw-Hill, New York, 1997).
30. Cai, N., Xi, J.-X., Zhong, Y.-S. & Ma, H.-Y. Controllability improvement for linear time-invariant dynamical multi-agent systems. Int. J. Innov. Comput. I 8, 3315-3328 (2012).
31. Parlangeli, G.&Notarstefano, G. On the reachability and observability of path and cycle graphs. IEEE Trans. Autom. Control 57, 743-748 (2012).
32. Notarstefano, G. & Parlangeli, G. Controllability and observability of grid graphs via reduction and symmetries. IEEE Trans. Autom. Control 58, 1719-1731 (2013).
33. Slotine, J.-J.&Li, W. Applied Nonlinear Control (Prentice-Hall, New Jersey, 1991).
34. Murota, K. Matrices and Matroids for Systems Analysis (Springer, New York, 2000).