Eur. Phys. J. D 40, 417-422 (2006)
https://doi.org/10.1140/epjd/e2006-00160-9

Multiple Devil's staircase in a discontinuous circle map

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

Corresponding author: ^a wxmwang@nxu.edu.cn

Received: 6 February 2006
Revised: 15 May 2006
Published online: 12 July 2006

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.