Multiple Devil's staircase in a discontinuous circle map |
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Authors: | X.-M. Wang Z.-J. Fang J.-F. Zhang |
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Affiliation: | (1) School of Physics and Electric Information, NingXia University, Yinchuan, 750021, P.R. China;(2) School of Sciences, HeBei University of Technology, Tianjin, 300130, P.R. China |
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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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Keywords: | 05.45.Ac Low-dimensional chaos |
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