中国物理B ›› 2018, Vol. 27 ›› Issue (10): 100502-100502.doi: 10.1088/1674-1056/27/10/100502

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇    下一篇

Phase order in one-dimensional piecewise linear discontinuous map

Ru-Hai Du(杜如海), Sheng-Jun Wang(王圣军), Tao Jin(金涛), Shi-Xian Qu(屈世显)   

  1. 1 Institute of Theoretical & Computational Physics, Shaanxi Normal University, Xi'an 710119, China;
    2 School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710119, China
  • 收稿日期:2018-05-02 修回日期:2018-07-17 出版日期:2018-10-05 发布日期:2018-10-05
  • 通讯作者: Shi-Xian Qu E-mail:sxqu@snnu.edu.cn
  • 基金资助:

    Project supported by the National Natural Science Foundation of China (Grant No. 11645005) and the Interdisciplinary Incubation Project of Shaanxi Normal University (Grant No. 5).

Phase order in one-dimensional piecewise linear discontinuous map

Ru-Hai Du(杜如海)1,2, Sheng-Jun Wang(王圣军)1,2, Tao Jin(金涛)1,2, Shi-Xian Qu(屈世显)1,2   

  1. 1 Institute of Theoretical & Computational Physics, Shaanxi Normal University, Xi'an 710119, China;
    2 School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710119, China
  • Received:2018-05-02 Revised:2018-07-17 Online:2018-10-05 Published:2018-10-05
  • Contact: Shi-Xian Qu E-mail:sxqu@snnu.edu.cn
  • Supported by:

    Project supported by the National Natural Science Foundation of China (Grant No. 11645005) and the Interdisciplinary Incubation Project of Shaanxi Normal University (Grant No. 5).

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摘要：

The phase order in a one-dimensional (1D) piecewise linear discontinuous map is investigated. The striking feature is that the phase order may be ordered or disordered in multi-band chaotic regimes, in contrast to the ordered phase in continuous systems. We carried out an analysis to illuminate the underlying mechanism for the emergence of the disordered phase in multi-band chaotic regimes, and proved that the phase order is sensitive to the density distribution of the trajectories of the attractors. The scaling behavior of the net direction phase at a transition point is observed. The analytical proof of this scaling relation is obtained. Both the numerical and analytical results show that the exponent is 1, which is controlled by the feature of the map independent on whether the system is continuous or discontinuous. It extends the universality of the scaling behavior to systems with discontinuity. The result in this work is important to understanding the property of chaotic motion in discontinuous systems.

关键词: chaos, piecewise discontinuous map, direction phase

Abstract:

The phase order in a one-dimensional (1D) piecewise linear discontinuous map is investigated. The striking feature is that the phase order may be ordered or disordered in multi-band chaotic regimes, in contrast to the ordered phase in continuous systems. We carried out an analysis to illuminate the underlying mechanism for the emergence of the disordered phase in multi-band chaotic regimes, and proved that the phase order is sensitive to the density distribution of the trajectories of the attractors. The scaling behavior of the net direction phase at a transition point is observed. The analytical proof of this scaling relation is obtained. Both the numerical and analytical results show that the exponent is 1, which is controlled by the feature of the map independent on whether the system is continuous or discontinuous. It extends the universality of the scaling behavior to systems with discontinuity. The result in this work is important to understanding the property of chaotic motion in discontinuous systems.

Key words: chaos, piecewise discontinuous map, direction phase

中图分类号:  (Numerical simulations of chaotic systems)

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