Advertisement

The European Physical Journal D

, Volume 50, Issue 1, pp 75–80 | Cite as

Chaotic dynamics of a parametrically modulated Josephson junction with quadratic damping

  • F. LiEmail author
  • B. J. Zhou
  • W. X. Shu
  • H. L. Luo
  • Z. Y. Huang
  • L. Tian
Nonlinear Dynamics

Abstract

We study the chaotic dynamics of a parametrically modulated Josephson junction with quadratic damping. The Melnikov chaotic criteria are presented. When the perturbation conditions cannot be satisfied, numerical simulations demonstrate that the system can step into chaos via a quasi-periodic route with the increasing of the dc component of the modulation. However, it is numerically demonstrated that adding a feedback to the system can effectively suppress the chaos.

PACS

85.25.Cp Josephson devices 05.45.Ac Low-dimensional chaos 05.45.Gg Control of chaos, applications of chaos 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. V.N. Belykh, N.F. Pedersen, O.H. Soerensen, Phys. Rev. B 16, 4853 (1977); V.N. Belykh, N.F. Pedersen, O.H. Soerensen, Phys. Rev. B 16, 4860 (1977)Google Scholar
  2. B.A. Huberman, J.A. Crutchfield, N.H. Packard, Appl. Phys. Lett. 37, 750 (1980)Google Scholar
  3. V.N. Gubankov, K.I. Konstantinyan, V.P. Koshelets, G.A. Ovsyannikov, IEEE. Trans. Magn. 19, 637 (1983)Google Scholar
  4. Z.G. Genchev, Z.G. Ivanov, B.N. Todorov, IEEE Trans. Circuits Syst. 30, 633 (1983)Google Scholar
  5. M. Cirillo, N.F. Pedersen, Phys. Lett. A 90, 150 (1982)Google Scholar
  6. M. Octavio, Phys. Rev. B 29, 1231 (1984)Google Scholar
  7. M. Bartuccelli, P.L. Christiansen, N.F. Pedersen, M.P. Soerensen, Phys. Rev. B 33, 4686 (1986)Google Scholar
  8. G. Cicogna, L. Fronzoni, Phys. Rev. A 42, 1901 (1990)Google Scholar
  9. G. Cicogna, Phys. Lett. A 121, 403 (1987)Google Scholar
  10. G. Cicogna, Phys. Lett. A 131, 98 (1988)Google Scholar
  11. R.K. John, V.C. Kuriakose, K.B. Joseph, Phys. Lett. A 149, 211 (1990)Google Scholar
  12. X. Yao, J.Z. Wu, C.S. Ting, Phys. Rev. B 42, 244 (1990)Google Scholar
  13. T. Hesselroth, Phys. Rev. E 48, 46 (1993)Google Scholar
  14. W. Hai, Y. Xiao, J. Fang, W. Huang, X. Zhang, Phys. Lett. A 265, 128 (2000)Google Scholar
  15. W. Hai, X. Zhang, W. Huang, G. Chong, Int. J. Bifur. Chaos 11, 2263 (2001)Google Scholar
  16. W. Hai, Y. Xiao, G. Chongand, Q. Xie, Phys. Lett. A 295, 220 (2002)Google Scholar
  17. K. Yu, J. Zou, B. Shao, Chin. Phys. 10, 1154 (2001)Google Scholar
  18. Y. Xuan, Z. Li, H. Tao, Z. Ren, G. Che, B. Zhao, Z. Zhao, Chin. Phys. Lett. 18, 1254 (2001)Google Scholar
  19. Y. Zhan, Chin. Phys. 14, 1044 (2005)Google Scholar
  20. T. Zhou, S. Yan, L. Fang, X. Zuo, S. Li, L. Ji, X. Zhao, Chin. Phys. Lett. 23, 1935 (2006)Google Scholar
  21. T. Zeng, B. Shao, P. Chang, J. Zou, Chin. Phys. Lett. 23, 2644 (2006)Google Scholar
  22. Q. Wu, F. Li, Chin. Phys. Lett. 27, 640 (2007)Google Scholar
  23. C.R. Nayak, V.C. Kuriakose, Phys. Lett. A 365, 284 (2007)Google Scholar
  24. C.W. Lim, S.K. Lai, Phys. Lett. A 368, 289 (2007)Google Scholar
  25. W. Hai, C. Lee, G. Chong, L. Shi, Phys. Rev. E 66, 026202 (2002)Google Scholar
  26. J. Fang, W. Hai, G. Chong, Q. Xie, Physica A 349, 133 (2005)Google Scholar
  27. F. Li, W. Shu, J. Jiang, H. Luo, Z. Ren, Eur. Phys. J. D 41, 355 (2007)Google Scholar
  28. F. Li, W. Shu, H. Luo, Z. Ren, Chin. Phys. 16, 650 (2007)Google Scholar
  29. F. Li, Z. Ren, H. Luo, W. Shu, Q. Wu, Commun. Theor. Phys. 48, 107 (2007)Google Scholar
  30. J. Guckenheimer, P.J. Holmes, Nonlinear Oscillation, Dynamical System, and Bifurcation of Vector Field, Applied Mathematical Sciences, Vol. 42 (Springer-Verlag, Berlin, 1983)Google Scholar
  31. E. Bollt, Y. Lai, C.O. Grebogi, Phys. Rev. Lett. 79, 3787 (1997)Google Scholar
  32. J.G. Ojalvo, R. Roy, Phys. Rev. Lett. 86, 5204 (2001)Google Scholar

Copyright information

© Springer 2008

Authors and Affiliations

  • F. Li
    • 1
    Email author
  • B. J. Zhou
    • 1
  • W. X. Shu
    • 2
  • H. L. Luo
    • 2
  • Z. Y. Huang
    • 1
  • L. Tian
    • 1
  1. 1.Department of PhysicsHunan University of Science and TechnologyXiangtanP.R. China
  2. 2.School of Computer and Communication, Hunan UniversityChangshaP.R. China

Personalised recommendations