Time-frequency analysis of chaotic systems

被引：127
|
作者：
Chandre, C
Wiggins, S
Uzer, T
机构：
[1] CNRS, Ctr Phys Theor, F-13288 Marseille 09, France
[2] Univ Bristol, Dept Math, Bristol BS8 1TW, Avon, England
[3] Georgia Inst Technol, Sch Phys, Ctr Nonlinear Sci, Atlanta, GA 30332 USA
来源：
PHYSICA D-NONLINEAR PHENOMENA | 2003年 / 181卷 / 3-4期
关键词：
time-frequency analysis; wavelets; Hamiltonian systems;
D O I：
10.1016/S0167-2789(03)00117-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We describe a method for analyzing the phase space structures of Hamiltonian systems. This method is based on a time-frequency decomposition of a trajectory using wavelets. The ridges of the time-frequency landscape of a trajectory, also called instantaneous frequencies, enable us to analyze the phase space structures. In particular, this method detects resonance trappings and transitions and allows a characterization of the notion of weak and strong chaos. We illustrate the method with the trajectories of the standard map and the hydrogen atom in crossed magnetic and elliptically polarized microwave fields. (C) 2003 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：171 / 196
页数：26
相关论文
共 50 条
  • [1] Analysis of chaotic signals in the time-frequency plane
    Galleani, L
    Biey, M
    Gilli, M
    Lo Presti, L
    [J]. PROCEEDINGS OF THE IEEE-EURASIP WORKSHOP ON NONLINEAR SIGNAL AND IMAGE PROCESSING (NSIP'99), 1999, : 100 - 104
  • [2] Windowing Systems for Time-Frequency Analysis
    Stephen D. Casey
    [J]. Sampling Theory in Signal and Image Processing, 2012, 11 (2-3): : 221 - 251
  • [3] From phase space to frequency domain: A time-frequency analysis for chaotic time series
    Sun, Junfeng
    Zhao, Yi
    Nakamura, Tomomichi
    Small, Michael
    [J]. PHYSICAL REVIEW E, 2007, 76 (01)
  • [4] \ Analysis of chaotic system characters based on time-frequency distribution
    Nie, Chunyan
    Shi, Yaowu
    Yi, Wensuo
    [J]. WCICA 2006: SIXTH WORLD CONGRESS ON INTELLIGENT CONTROL AND AUTOMATION, VOLS 1-12, CONFERENCE PROCEEDINGS, 2006, : 4842 - +
  • [5] SIMULTANEOUS TIME-FREQUENCY SYNCHRONIZATION OF NON-AUTONOMOUS CHAOTIC SYSTEMS
    Liu, Meng-Kun
    Suh, C. Steve
    [J]. PROCEEDINGS OF THE ASME INTERNATIONAL MECHANICAL ENGINEERING CONGRESS AND EXPOSITION, 2013, VOL 4B, 2014,
  • [6] Time-frequency analysis of time-variant systems
    [J]. 2013, Polish Society of Technical Diagnostics (14):
  • [7] ANALYSIS OF THE PROPERTIES OF TIME-FREQUENCY SIGNALS SYSTEMS
    PYSHKIN, IM
    PANTIKYAN, RT
    [J]. RADIOTEKHNIKA I ELEKTRONIKA, 1983, 28 (01): : 82 - 85
  • [8] Time-Frequency Processing Key Technologies in Time-Frequency Related Systems
    Zhou, Wei
    Li, Xiaodong
    Li, Zishuai
    Jia, Lifeng
    Liu, Chen
    Li, Xiaoyu
    [J]. CSNC 2011: 2ND CHINA SATELLITE NAVIGATION CONFERENCE, VOLS 1-3, 2011, : 687 - 693
  • [9] Fault diagnosis of circuit breakers based on time-frequency and chaotic vibration analysis
    Yang, Qiuyu
    Ruan, Jiangjun
    Zhuang, Zhijian
    [J]. IET GENERATION TRANSMISSION & DISTRIBUTION, 2020, 14 (07) : 1214 - 1221
  • [10] Time-frequency analysis of transient signals in power distribution systems
    Danisor, Alin
    [J]. ADVANCED TOPICS IN OPTOELECTRONICS, MICROELECTRONICS, AND NANOTECHNOLOGIES VIII, 2016, 10010
12345