Advertisement

Inducing amplitude death via pinning control

  • Nannan Zhao
  • Zhongkui SunEmail author
  • Wei Xu
Regular Article
  • 54 Downloads

Abstract

The amplitude death (AD) phenomenon is an important dynamical behavior. Seeking the generation condition that induces AD has been an active and popular research field over the last two decades. In this paper, we report the emergence of AD in the identical coupled system with different network topologies through the pinning control. Using the negative self-feedback as the controllers to pin the network nodes, the critical condition that AD appears can be obtained theoretically. Moreover, the numerical scenarios, such as a single oscillator, two coupled oscillators, and coupled oscillators in regular and complex networks, have also been carried out to validate the effectiveness of the strategy, which coincides with the theoretical predictions. We show that, although the high degree nodes should be pinned preferentially to reach better efficiency for complex networks, the location (or significance) of nodes in network is more noteworthy than the degree of nodes for some regular networks. Our findings therefore provide a possibility to induce AD in coupled systems with different network topologies whose internal parameters and coupling schemes cannot be modified.

Graphical abstract

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    A. Pikovsky, M. Rosenblum, J. Kurths,Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, 2003) Google Scholar
  2. 2.
    Y. Kuramoto,Chemical oscillations, waves, and turbulence (Springer, Berlin, 1984) Google Scholar
  3. 3.
    S. Boccaletti, J. Kurths, G. Osipov, D.L. Valladares, C. Zhou, Phys. Rep. 366, 1 (2002) ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    A. Arenas, A. Díaz-Guilera, J. Kurths, Y. Moreno, C. Zhou, Phys. Rep. 469, 93 (2008) ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    D.M. Abrams, S.H. Strogatz, Phys. Rev. Lett. 93, 174102 (2004) ADSCrossRefGoogle Scholar
  6. 6.
    D.M. Abrams, R. Mirollo, S.H. Strogatz, D.A. Wiley, Phys. Rev. Lett. 101, 084103 (2008) ADSCrossRefGoogle Scholar
  7. 7.
    H. Daido, K. Nakanishi, Phys. Rev. Lett. 93, 104101 (2004) ADSCrossRefGoogle Scholar
  8. 8.
    H. Daido, Phys. Rev. E 84, 016215 (2011) ADSCrossRefGoogle Scholar
  9. 9.
    H. Daido, Europhys. Lett. 84, 10002 (2008) ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    G. Saxena, A. Prasad, R. Ramaswamy, Phys. Rep. 521, 205 (2012) ADSCrossRefGoogle Scholar
  11. 11.
    A. Koseska, E. Volkov, J. Kurths, Phys. Rev. Lett. 111, 024103 (2013) ADSCrossRefGoogle Scholar
  12. 12.
    A. Koseska, E. Volkov, J. Kurths, Phys. Rep. 531, 173 (2013) ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    A. Prasad, Y.C. Lai, A. Gavrielides, V. Kovanis, Phys. Lett. A 318, 71 (2003) ADSCrossRefGoogle Scholar
  14. 14.
    G.B. Ermentrout, N. Kopell, SIAM J. Appl. Math. 50, 125 (1990) MathSciNetCrossRefGoogle Scholar
  15. 15.
    N. Suzuki, C. Furusawa, K. Kaneko, PloS ONE 6, e27232 (2011) ADSCrossRefGoogle Scholar
  16. 16.
    E. Ullner, A. Zaikin, E.I. Volkov, J. García-Ojalvo, Phys. Rev. Lett. 99, 148103 (2007) ADSCrossRefGoogle Scholar
  17. 17.
    D.G. Aronson, G.B. Ermentrout, N. Kopell, Physica D 41, 403 (1990) ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    R.E. Mirollo, S.H. Strogatz, J. Stat. Phys. 60, 245 (1990) ADSCrossRefGoogle Scholar
  19. 19.
    D.V. Ramana Reddy, A. Sen, G.L. Johnston, Phys. Rev. Lett. 80, 5109 (1998) ADSCrossRefGoogle Scholar
  20. 20.
    W. Zou, X. Zheng, M. Zhan, Chaos 21, 023130 (2011) ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    G. Saxena, A. Prasad, R. Ramaswamy, Phys. Rev. E 82, 017201 (2010) ADSCrossRefGoogle Scholar
  22. 22.
    R. Karnatak, R. Ramaswamy, A. Prasad, Phys. Rev. E 76, 432 (2007) CrossRefGoogle Scholar
  23. 23.
    N. Zhao, Z. Sun, X. Yang, W. Xu, Europhys. Lett. 118, 30005 (2017) ADSCrossRefGoogle Scholar
  24. 24.
    K. Konishi, Phys. Rev. E 68, 13 (2003) CrossRefGoogle Scholar
  25. 25.
    N. Zhao, Z. Sun, W. Xu, Eur. Phys. J. B 91, 20 (2018) ADSCrossRefGoogle Scholar
  26. 26.
    S. Rakshit, B.K. Bera, S. Majhi, C. Hens, D. Ghosh, Sci. Rep. 7, 45909 (2017) ADSCrossRefGoogle Scholar
  27. 27.
    Z. Sun, N. Zhao, X. Yang, W. Xu, Nonlinear Dyn. 92, 1185 (2018) CrossRefGoogle Scholar
  28. 28.
    R.O. Grigoriev, M.C. Cross, H.G. Schuster, Phys. Rev. Lett. 79, 2795 (1997) ADSCrossRefGoogle Scholar
  29. 29.
    H. Su, X. Wang,Pinning control of complex networked systems: Synchronization, consensus and flocking of networked systems via pinning (Springer, Berlin, 2013) Google Scholar
  30. 30.
    X. Wang, G. Chen, Physica A 310, 521 (2002) ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    X. Li, X. Wang, G. Chen, IEEE Trans. Circuits Syst. I 51, 2074 (2004) CrossRefGoogle Scholar
  32. 32.
    Z. Rong, X. Li, W. Lu, inIEEE International Symposium on Circuits and Systems (IEEE, 2009), p. 1689 Google Scholar
  33. 33.
    X. Wang, H. Su, Annu. Rev. Control 38, 103 (2014) CrossRefGoogle Scholar
  34. 34.
    D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998) ADSCrossRefGoogle Scholar
  35. 35.
    A.L. Barabási, R. Albert, Science 286, 509 (1999) ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Applied MathematicsNorthwestern Polytechnical UniversityXi’anP.R. China

Personalised recommendations