Advertisement

The coupled dynamics of two particles with different limit sets

  • Colm Mulhern
  • Dirk Hennig
  • Andrew David Burbanks
Regular Article

Abstract

We consider a system of two coupled particles evolving in a periodic and spatially symmetric potential under the influence of external driving and damping. The particles are driven individually in such a way that in the uncoupled regime, one particle evolves on a chaotic attractor, while the other evolves on regular periodic attractors. Notably, only the latter supports coherent particle transport. The influence of the coupling between the particles is explored, and in particular how it relates to the emergence of a directed current. We show that increasing the (weak) coupling strength subdues the current in a process, which in phase-space, is related to a merging crisis of attractors forming one large chaotic attractor in phase-space. Further, we demonstrate that complete current suppression coincides with a chaos-hyperchaos transition.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    W. Acevedo, T. Dittrich, Prog. Theor. Phys. Suppl. 150, 313 (2003)MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    H. Schanz, M. Prusty, J. Phys. A 38, 10085 (2005)MathSciNetADSzbMATHCrossRefGoogle Scholar
  3. 3.
    M. Horvat, T. Prosen, J. Phys. A 37, 3133 (2004)MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. 4.
    P. Reimann, Phys. Rep. 361, 57 (2002)MathSciNetADSzbMATHCrossRefGoogle Scholar
  5. 5.
    D. Hennig, A.D. Burbanks, A.H. Osbaldestin, C. Mulhern, J. Phys. A 43, 345101 (2010)MathSciNetCrossRefGoogle Scholar
  6. 6.
    D. Hennig, A.D. Burbanks, A.H. Osbaldestin, Physica D 238, 2273 (2009)MathSciNetADSzbMATHCrossRefGoogle Scholar
  7. 7.
    J.B. Majer et al., Phys. Rev. Lett. 90, 056802 (2003)ADSCrossRefGoogle Scholar
  8. 8.
    R.D. Austumian, P. Hänggi, Phys. Today 55, 33 (2002)CrossRefGoogle Scholar
  9. 9.
    P. Hänggi, F. Marchesoni, Rev. Mod. Phys. 81, 387 (2009)ADSCrossRefGoogle Scholar
  10. 10.
    C. Beck, Physica C 473, 21 (2012)ADSCrossRefGoogle Scholar
  11. 11.
    S. Fugmann, D. Hennig, L. Schimansky-Geier, I.M. Sokolov, Eur. Phys. J. Special Topics 191, 187 (2010)ADSCrossRefGoogle Scholar
  12. 12.
    A. Smerzi, S. Fantoni, S. Giovanazzi, S.R. Shenoy, Phys. Rev. Lett. 79, 4950 (1997)ADSCrossRefGoogle Scholar
  13. 13.
    E. Ott, Chaos in Dynamical Systems (Cambridge University Press, New York, 1993)Google Scholar
  14. 14.
    S. Yanchuk, T. Kapitaniak, Phys. Lett. A 290, 139 (2001)ADSzbMATHCrossRefGoogle Scholar
  15. 15.
    D. Hennig, A.D. Burbanks, A.H. Osbaldestin, C. Mulhern, Chaos 21, 023132 (2011)MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    J.L. Mateos, Phys. Rev. Lett. 84, 258 (2000)ADSCrossRefGoogle Scholar
  17. 17.
    J.L. Mateos, Physica A 325, 92 (2003)MathSciNetADSzbMATHCrossRefGoogle Scholar
  18. 18.
    A. Kenfack, S.M. Sweetman, A.K. Pattanayak, Phys. Rev. E 75, 056215 (2007)ADSCrossRefGoogle Scholar
  19. 19.
    T.S. Parker, L.O. Chua, Practical Numerical Algorithms for Chaotic Systems (Springer-Verlag, New York, 1989)Google Scholar
  20. 20.
    O. Yevtushenko, S. Flach, K. Richter, Phys. Rev. E 61, 7215 (2000)ADSCrossRefGoogle Scholar
  21. 21.
    S. Denisov, S. Flach, A.A. Ovchinnikov, O. Yevtushenko, Y. Zolotaryuk, Phys. Rev. E 66, 041104 (2002)ADSCrossRefGoogle Scholar
  22. 22.
    D. Hennig, L. Schimansky-Geier, P. Hänggi, Eur. Phys. J. B 62, 493 (2008)ADSCrossRefGoogle Scholar
  23. 23.
    D. Hennig, L. Schimansky-Geier, P. Hänggi, Europhys. News 39, 21 (2008)CrossRefGoogle Scholar
  24. 24.
    C. Grebogi, E. Ott, J.A. Yorke, Phys. Rev. Lett. 48, 1507 (1982)MathSciNetADSCrossRefGoogle Scholar
  25. 25.
    J.A. Yorke, Physica D 7, 181 (1983)MathSciNetADSCrossRefGoogle Scholar
  26. 26.
    F. Romeiras, J.A. Yorke, Phys. Rev. A 36, 5365 (1987)MathSciNetADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Colm Mulhern
    • 1
  • Dirk Hennig
    • 1
  • Andrew David Burbanks
    • 1
  1. 1.Department of MathematicsUniversity of PortsmouthPortsmouthUK

Personalised recommendations