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Numerical Calculations for Nonlinear Characteristics of Chaotic Systems

Received: 1 December 2015     Published: 1 December 2015
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Abstract

This paper describes the relationship between Lyapunov index and the chaos of the dynamics system. Mainly describe the Lorenz system and Rossler system, and calculated the Lyapunov index of these two systems with nonlinear dynamics method. Analyses the iterative chaotic characteristic of Logistic system. And then calculate the Lyapunov index with the discrete system Lyapunov index computing method, and then calculated the correlation dimension.

Published in Journal of Electrical and Electronic Engineering (Volume 3, Issue 5)
DOI 10.11648/j.jeee.20150305.19
Page(s) 150-155
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Lorenz System, Rossler System, Logistic System, Correlation Dimensions, Lyapunov Index

References
[1] 洪奕光.非线性控制系统的若干分析和综合方法[J].系统科学与数学.2012,12:1497-1503。
[2] 伊利亚•普里戈金. 确定性的终结:时间、混沌与新自然法则[M].上海科技教育出版社.2009。
[3] 高思莉,肖青,齐欣,等.逻辑斯蒂映像混沌区的几个非线性特征量[J].新乡师范高等专科学校学报,2003,02:10-14。
[4] 赫希.微分方程、动力系统与混沌导论[M].人民邮电出版社,2008。
[5] 李尧亭,蔡诗东.混沌和李雅谱诺夫特征指数[J].物理, 1996, 05(5):0-0。
[6] King C C. Fractal and chaotic dynamics in nervous systems[J]. Progress in Neurobiology, 1991, 36(4):279–308。
[7] 廖晓昕,罗琦.Lorenz混沌系统Lyapunov稳定性简洁的代数充要条件及其应用[J].中国科学:信息科学,2010,08(8):1086-1095。
[8] 尤晓玲.Rossler系统的动力学行为研究及混沌抑制[J]. 工业仪表与自动化装置,2013,04:6-8。
[9] 王云雄,翁贻方,郑德玲.混沌的复杂度研究方法和Logistic映射分析[J].北京工商大学学报:自然科学版,2006,2:38-41。
[10] 王立明.二维logistic映射的动力学行为和奇怪吸引子的分形特征[J].大学物理,2010,2:21-25。
Cite This Article
  • APA Style

    Ma Shangang, Jin Fubao, Liang Bin, Tang Yan. (2015). Numerical Calculations for Nonlinear Characteristics of Chaotic Systems. Journal of Electrical and Electronic Engineering, 3(5), 150-155. https://doi.org/10.11648/j.jeee.20150305.19

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    ACS Style

    Ma Shangang; Jin Fubao; Liang Bin; Tang Yan. Numerical Calculations for Nonlinear Characteristics of Chaotic Systems. J. Electr. Electron. Eng. 2015, 3(5), 150-155. doi: 10.11648/j.jeee.20150305.19

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    AMA Style

    Ma Shangang, Jin Fubao, Liang Bin, Tang Yan. Numerical Calculations for Nonlinear Characteristics of Chaotic Systems. J Electr Electron Eng. 2015;3(5):150-155. doi: 10.11648/j.jeee.20150305.19

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  • @article{10.11648/j.jeee.20150305.19,
      author = {Ma Shangang and Jin Fubao and Liang Bin and Tang Yan},
      title = {Numerical Calculations for Nonlinear Characteristics of Chaotic Systems},
      journal = {Journal of Electrical and Electronic Engineering},
      volume = {3},
      number = {5},
      pages = {150-155},
      doi = {10.11648/j.jeee.20150305.19},
      url = {https://doi.org/10.11648/j.jeee.20150305.19},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.jeee.20150305.19},
      abstract = {This paper describes the relationship between Lyapunov index and the chaos of the dynamics system. Mainly describe the Lorenz system and Rossler system, and calculated the Lyapunov index of these two systems with nonlinear dynamics method. Analyses the iterative chaotic characteristic of Logistic system. And then calculate the Lyapunov index with the discrete system Lyapunov index computing method, and then calculated the correlation dimension.},
     year = {2015}
    }
    

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  • TY  - JOUR
    T1  - Numerical Calculations for Nonlinear Characteristics of Chaotic Systems
    AU  - Ma Shangang
    AU  - Jin Fubao
    AU  - Liang Bin
    AU  - Tang Yan
    Y1  - 2015/12/01
    PY  - 2015
    N1  - https://doi.org/10.11648/j.jeee.20150305.19
    DO  - 10.11648/j.jeee.20150305.19
    T2  - Journal of Electrical and Electronic Engineering
    JF  - Journal of Electrical and Electronic Engineering
    JO  - Journal of Electrical and Electronic Engineering
    SP  - 150
    EP  - 155
    PB  - Science Publishing Group
    SN  - 2329-1605
    UR  - https://doi.org/10.11648/j.jeee.20150305.19
    AB  - This paper describes the relationship between Lyapunov index and the chaos of the dynamics system. Mainly describe the Lorenz system and Rossler system, and calculated the Lyapunov index of these two systems with nonlinear dynamics method. Analyses the iterative chaotic characteristic of Logistic system. And then calculate the Lyapunov index with the discrete system Lyapunov index computing method, and then calculated the correlation dimension.
    VL  - 3
    IS  - 5
    ER  - 

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Author Information
  • School of Water Resources and Electric Power, Qinghai University, Xining, China

  • School of Water Resources and Electric Power, Qinghai University, Xining, China

  • School of Water Resources and Electric Power, Qinghai University, Xining, China

  • School of Water Resources and Electric Power, Qinghai University, Xining, China

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