Applied Mathematics and Mechanics

, Volume 20, Issue 11, pp 1214–1221 | Cite as

The non-linear chaotic model reconstruction for the experimental data obtained from different dynamic system

  • Ma Juhai
  • Chen Yushu
  • Liu Zengrong


The non-linear chaotic model reconstruction is the major important quantitative index for describing accurate experimental data obtained in dynamic analysis. A lot of work has been done to distinguish chaos from randomness, to calulate fractral dimension and Lyapunov exponent, to reconstruct the state space and to fix the rank of model. In this paper, a new improved EAR method is presented in modelling and predicting chaotic timeseries, and a successful approach to fast estimation algorithms is proposed. Some illustrative experimental data examples from known chaotic systems are presented, emphasising the increase in predicting error with time. The calculating results tell us that the parameter identification method in this paper can effectively adjust the initial value towards the global limit value of the single peak target function nearby. The the model paremeter can immediately be obtained by using the improved optimization method rapidly, and non-linear chaotic models can not provide long period superior predictions. Applications of this method are listed to real data from widely different areas.

Key words

non-linear chaotic timeseries Lyapunov exponent chaotic model parameter identification CLC number O175.14 O241.81 


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  1. [1]
    Wu Ya, Yang Shuzi. Application of several timeseries models in prediction[A].Applied Time Series Analysis[M]. Beijing: World Scientific Publishing, 1989.Google Scholar
  2. [2]
    Chen C H.Applied Timeseries Analysis[M]. Beijing: World Scientific Publishing Cor, 1989.Google Scholar
  3. [3]
    Yang Shuzi, Yu Ya.Applied Timeseries Analysis in Engineering[M]. Beijing: World Scientific Publishing Cor, 1992.Google Scholar
  4. [4]
    Ma Junhai, Chen Yushu, Liu Zengrong. The threshold value for diagnosis of chaotic nature of the data obtained i nonlinear dynamic analysis [J].Applied Mathematics and Mechanics (English Ed), 1998,19(6):513–520.CrossRefGoogle Scholar
  5. [5]
    Nerenberg M A H. Correlation dimension and systematic geometric effects[J].Phys Rev A, 1990,42(6):7065–7674.MathSciNetCrossRefGoogle Scholar
  6. [6]
    Alan Wolf, et al. Determining Lyapunov exponent from a timeseries[J].Phys D, 1985,16(9):285–317.MATHMathSciNetCrossRefGoogle Scholar
  7. [7]
    Mess A I, et al. Singular-value decomposition and embedding dimension[J].Phys Rev A, 1987,36(1):340–347.CrossRefGoogle Scholar
  8. [8]
    Ma Junhai.The Non-Linear Dynamic System Reconstruction of the Chaotic Timeseries, A Thesis for Degree of Engineering[D]. Tianjin: Tianjin University, 1997, 5. (in Chinese)Google Scholar
  9. [9]
    Zhang Qinghua, Wavelet networks[J].IEE Transections on Neural Networks, 1992,6 (11):889–898.Google Scholar
  10. [10]
    Liang Yuecao. Predicting chaotic timeseries with wavelet networks[J].Phys. D, 1995,85(8):225–238.Google Scholar
  11. [11]
    Dean Prichard. Generating surrogate date for time series with several simultaneously measured variables[J].Phys Rev Lett, 1994,191(7):230–245.Google Scholar
  12. [12]
    Davies M E. Reconstructing attractions from filtered time series[J].Phys D, 1997,101: 195–206.MATHMathSciNetCrossRefGoogle Scholar
  13. [13]
    Alexet Potapov. Distortions of reconstruction for chaotic attractors[J].Phys D, 1997,101 (5):207–226.MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1999

Authors and Affiliations

  • Ma Juhai
    • 1
  • Chen Yushu
    • 2
  • Liu Zengrong
    • 3
  1. 1.Department of Economy and ManagementTianjin Finance UniversityTianjinP R China
  2. 2.Department of MechanicsTianjin UniversityTranjinP R China
  3. 3.Department of MathematicsShanghai UniversityShanghaiP R China

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