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Node-to-node pinning control of complex networks

Chaos 19, 013122 (2009); doi:10.1063/1.3080192

Published 3 March 2009

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Maurizio Porfiri and Francesca Fiorilli
Department of Mechanical and Aerospace Engineering, Polytechnic Institute of New York University, Brooklyn, New York 11201, USA
In this paper, we study pinning controllability of oscillator networks. We present necessary conditions for network pinning controllability based on the spectral properties of the oscillator network and the individual oscillator dynamics. We define a performance metric for pinning-control systems based on the location of pinned sites, the pinning-control gains, and the network topology. We show that for any network structure, uniform pinning of all the network nodes maximizes the pinning-control performance. We propose the node-to-node pinning-control strategy to optimize the control performance while avoiding to simultaneously control all the network sites. In this novel strategy, the pinning-control action rapidly switches from one node to another with the goal of taming the oscillator network dynamics to the desired trajectory. We illustrate our findings through numerical simulations on networks of Rössler oscillators. ©2009 American Institute of Physics
History: Received 8 August 2008; accepted 20 January 2009; published 3 March 2009
Permalink: http://link.aip.org/link/?CHAOEH/19/013122/1
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KEYWORDS and PACS

Keywords
PACS
  • 05.45.Xt
    Synchronization; coupled oscillators (nonlinear dynamical systems)
  • 05.90.+m
    Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems
  • 89.75.Fb
    Structures and organization in complex systems
  • 02.60.-x
    Numerical approximation and analysis
  • YEAR: 2009

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PUBLICATION DATA

ISSN:
1054-1500 (print)   1089-7682 (online)
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REFERENCES (38)
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  1. R. Grigoriev, M. Cross, and H. Schuste, Phys. Rev. Lett. 79, 2795 (1997).
  2. X. Wang and G. Chen, Physica A 310, 521 (2002).
  3. X. Li, X. Wang, and G. Chen, IEEE Trans. Circuits Syst., I: Regul. Pap. 51, 2074 (2004).
  4. T. Chen, X. Liu, and W. Lu, IEEE Trans. Circuits Syst., I: Regul. Pap. 54, 1317 (2007).
  5. W. Lu, Chaos 17, 023122 (2007).
  6. J. Xiang and G. Chen, Automatica 43, 1049 (2007).
  7. R. Li, Z. Duan, and G. Chen, Chin. Phys. B 18, 106 (2009).
  8. F. Sorrentino, Chaos 17, 033101 (2007).
  9. F. Sorrentino, M. Di Bernardo, F. Garofalo, and G. Chen, Phys. Rev. E 75, 046103 (2007).
  10. M. Porfiri and M. Di Bernardo, Automatica 44, 3100 (2008).
  11. P. De Lellis, M. Di Bernardo, and F. Garofalo, Chaos 18, 037110 (2008).
  12. C. W. Wu, in Proceedings of IEEE International Symposium on Circuits and Systems, 2008, pp. 2530–2533.
  13. L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 80, 2109 (1998).
  14. J. M. Gonzalez-Miranda, Synchronization and Control of Chaos (Imperial College Press, London, 2004).
  15. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D. Hwang, Phys. Rep. 424, 175 (2006).
  16. T. Nishikawa and A. E. Motter, Physica D 224, 77 (2006).
  17. D. J. Stilwell, E. M. Bollt, and D. G. Roberson, SIAM J. Appl. Dyn. Syst. 5, 140 (2006).
  18. L. Fortuna, M. Frasca, and A. Rizzo, Chaos, Solitons Fractals 17, 355 (2003).
  19. J. D. Skufca and E. M. Bollt, Math. Biosci. Eng. 1, 347 (2004).
  20. R. Amritkar and C. Hu, Chaos 16, 015117 (2006).
  21. M. Porfiri and D. J. Stilwell, IEEE Trans. Autom. Control 52, 1767 (2007).
  22. M. Porfiri and F. Fiorilli, “Global pulse synchronization of chaotic oscillators through fast-switching: theory and experiments,” Chaos, Solitons Fractals (in press).
  23. M. Porfiri and R. Pigliacampo, SIAM J. Appl. Dyn. Syst. 7, 825 (2008).
  24. M. Porfiri, D. J. Stilwell, and E. M. Bollt, IEEE Trans. Circuits Syst., I: Regul. Pap. 55, 3170 (2008).
  25. C. Godsil and G. Royle, Algebraic Graph Theory (Springer-Verlag, New York, 2001).
  26. R. Grone and R. Merris, SIAM J. Discrete Math. 7, 221 (1994).
  27. J. S. Li and X. D. Zhang, Linear Algebr. Appl. 285, 305 (1998).
  28. R. Merris, Linear Algebr. Appl. 285, 33 (1998).
  29. K. C. Das, Linear Algebr. Appl. 368, 269 (2003).
  30. N. M. M. de Abreu, Linear Algebr. Appl. 423, 5 (2007).
  31. L. Shi, Linear Algebr. Appl. 422, 755 (2007).
  32. T. Biyikoglu, J. Leydold, and P. F. Stadler, Laplacian Eigenvectors of Graphs (Springer-Verlag, New York, 2007).
  33. R. W. Beard and W. Ren, Distributed Consensus in Multi-vehicle Cooperative Control (Springer-Verlag, New York, 2007).
  34. D. S. Bernstein, Matrix Mathematics (Princeton University Press, Princeton, 2005).
  35. V. Batagelj and A. Mrvar, Pajek. Program for Analysis and Visualization of Large Networks. Reference Manual. List of Commands with Short Explanation. Version 1.22 (University of Ljubljana, Lujbiana, 2008).
  36. D. M. Pennock, G. W. Flake, S. Lawrence, E. J. Glover, and C. L. Giles, Proc. Natl. Acad. Sci. U.S.A. 99, 5207 (2002).
  37. P. N. McGraw and M. Menzinger, Phys. Rev. E 77, 031102 (2008).
  38. J. P. Eckmann and D. Ruelle, Rev. Mod. Phys. 57, 617 (1985).

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