Numerical Calculations for Nonlinear Characteristics of Chaotic Systems

Ma Shangang; Jin Fubao; Liang Bin; Tang Yan

doi:doi:10.11648/j.jeee.20150305.19

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Numerical Calculations for Nonlinear Characteristics of Chaotic Systems

Ma Shangang, Jin Fubao, Liang Bin, Tang Yan

Published in Journal of Electrical and Electronic Engineering (Volume 3, Issue 5)

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

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[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。
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[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。
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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

Ma Shangang

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

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

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

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

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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

Copy | Download

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

Copy | Download

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

Copy | Download

@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}
}

Copy | Download

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  -

Copy | Download