Phase order in one-dimensional piecewise linear discontinuous map  

作　　者：Ru-Hai Du Sheng-Jun Wang Tao Jin Shi-Xian Qu 杜如海;王圣军;金涛;屈世显(Institute of Theoretical & Computational Physics,Shaanxi Normal University;School of Physics and Information Technology,Shaanxi Normal University)

机构地区：[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

出　　处：《Chinese Physics B》2018年第10期240-244,共5页中国物理B（英文版）

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

摘　　要：The phase order in a one-dimensional（1 D） 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.The phase order in a one-dimensional（1 D） 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 

分 类 号：O415.5[理学—理论物理]