Multiple Devil's staircase in a discontinuous circle map

Nonlinear Dynamics


The multiple Devil's staircase, which describes phase-locking behavior, is observed in a discontinuous nonlinear circle map. Phase-locked steps form many towers with similar structure in winding number(W)-parameter(k) space. Each step belongs to a certain period-adding sequence that exists in a smooth curve. The Collision modes that determine steps and the sequence of mode transformations create a variety of tower structures and their particular characteristics. Numerical results suggest a scaling law for the width of phase-locked steps in the period-adding (W=n/(n+i), n,i∈int) sequences, that is, Δk(n)∝n (τ>0). And the study indicates that the multiple Devil's staircase may be common in a class of discontinuous circle maps.


05.45.Ac Low-dimensional chaos 


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  1. P. Bak, R. Bruinsma, Phys. Rev. Lett. 49, 249 (1982) MathSciNetCrossRefADSGoogle Scholar
  2. T. Gilbert, R.W. Gammon, Int. J. Bifur. Chaos 10, 155 (2000) CrossRefGoogle Scholar
  3. S. Lacis, J.C. Bacri, A. Cebes, R. Perzynski, Phys. Rev. E 55, 2640 (1997) CrossRefADSGoogle Scholar
  4. D.-R. He, D.-K. Wang, K.-J. Shi, C.-H. Yang, L.-Y. Chao, J.Y. Zhang, Phys. Lett. A 136, 363 (1989) MathSciNetCrossRefADSGoogle Scholar
  5. W.-J. Yeh, D.-R. He, Y.H. Kao, Phys. Rev. B 31, 1359 (1985) CrossRefADSGoogle Scholar
  6. P. Bak, Phys. Today 39, 38 (1986) ADSGoogle Scholar
  7. S.-X. Qu, S. Wu, D.-R. He, Phys. Lett. A 231, 152 (1997) MATHMathSciNetCrossRefADSGoogle Scholar
  8. S.-X. Qu, S. Wu, D.-R. He, Phys. Rev. E 57, 402 (1998) MathSciNetCrossRefADSGoogle Scholar
  9. C.-Y. Wu, S.-X. Qu, S. Wu, D.-R. He, Chin. Phys. Lett. 15, 246 (1998) CrossRefGoogle Scholar
  10. K. Kaneko, Prog. Theor. Phys. 68, 669 (1982) MATHMathSciNetCrossRefADSGoogle Scholar
  11. X.-M. Wang, J.-S. Mao, S.-X. Qu, Z. Zhou, D.-R. He, Phys. Lett. A 293, 151 (2002) MATHCrossRefADSGoogle Scholar
  12. X.-M. Wang, S.-X. Qu, D.-R. He, Int. J. Bifur. Chaos 15, 1677 (2005) MATHCrossRefGoogle Scholar
  13. S. Martin, W. Martienssen, Phys. Rev. Lett. 56, 1522 (1986) CrossRefADSGoogle Scholar
  14. H.E. Nusse, E. Ott, J.A. Yorke, Phys. Rev. E 49, 1073 (1994) MathSciNetCrossRefADSGoogle Scholar
  15. H. Lamba, C.J. Budd, Phys. Rev. E 50, 84 (1994) MathSciNetCrossRefADSGoogle Scholar

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© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Authors and Affiliations

  1. 1.School of Physics and Electric Information, NingXia UniversityYinchuanP.R. China
  2. 2.School of Sciences, HeBei University of TechnologyTianjinP.R. China

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