Abstract.
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 (τ>0). And the study indicates that the multiple Devil's staircase may be common in a class of discontinuous circle maps.
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References
P. Bak, R. Bruinsma, Phys. Rev. Lett. 49, 249 (1982)
T. Gilbert, R.W. Gammon, Int. J. Bifur. Chaos 10, 155 (2000)
S. Lacis, J.C. Bacri, A. Cebes, R. Perzynski, Phys. Rev. E 55, 2640 (1997)
D.-R. He, D.-K. Wang, K.-J. Shi, C.-H. Yang, L.-Y. Chao, J.Y. Zhang, Phys. Lett. A 136, 363 (1989)
W.-J. Yeh, D.-R. He, Y.H. Kao, Phys. Rev. B 31, 1359 (1985)
P. Bak, Phys. Today 39, 38 (1986)
S.-X. Qu, S. Wu, D.-R. He, Phys. Lett. A 231, 152 (1997)
S.-X. Qu, S. Wu, D.-R. He, Phys. Rev. E 57, 402 (1998)
C.-Y. Wu, S.-X. Qu, S. Wu, D.-R. He, Chin. Phys. Lett. 15, 246 (1998)
K. Kaneko, Prog. Theor. Phys. 68, 669 (1982)
X.-M. Wang, J.-S. Mao, S.-X. Qu, Z. Zhou, D.-R. He, Phys. Lett. A 293, 151 (2002)
X.-M. Wang, S.-X. Qu, D.-R. He, Int. J. Bifur. Chaos 15, 1677 (2005)
S. Martin, W. Martienssen, Phys. Rev. Lett. 56, 1522 (1986)
H.E. Nusse, E. Ott, J.A. Yorke, Phys. Rev. E 49, 1073 (1994)
H. Lamba, C.J. Budd, Phys. Rev. E 50, 84 (1994)
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Wang, XM., Fang, ZJ. & Zhang, JF. Multiple Devil's staircase in a discontinuous circle map. Eur. Phys. J. D 40, 417–422 (2006). https://doi.org/10.1140/epjd/e2006-00160-9
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DOI: https://doi.org/10.1140/epjd/e2006-00160-9