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Identification of chaotic systems by neural network with hybrid learning algorithm

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  • Pan, Shing-Tai
  • Lai, Chih-Chin

Abstract

Based on the genetic algorithm (GA) and steepest descent method (SDM), this paper proposes a hybrid algorithm for the learning of neural networks to identify chaotic systems. The systems in question are the logistic map and the Duffing equation. Different identification schemes are used to identify both the logistic map and the Duffing equation, respectively. Simulation results show that our hybrid algorithm is more efficient than that of other methods.

Suggested Citation

  • Pan, Shing-Tai & Lai, Chih-Chin, 2008. "Identification of chaotic systems by neural network with hybrid learning algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 233-244.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:1:p:233-244
    DOI: 10.1016/j.chaos.2006.08.037
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    References listed on IDEAS

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    1. Khaki-Sedigh, A. & Yazdanpanah-Goharrizi, A., 2006. "Observer-based design of set-point tracking adaptive controllers for nonlinear chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1063-1072.
    2. Park, Ju H. & Kwon, O.M., 2006. "Guaranteed cost control of time-delay chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 1011-1018.
    3. Vasegh, Nastaran & Majd, Vahid Johari, 2006. "Adaptive fuzzy synchronization of discrete-time chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 1029-1036.
    4. Li, Lixiang & Yang, Yixian & Peng, Haipeng & Wang, Xiangdong, 2006. "Parameters identification of chaotic systems via chaotic ant swarm," Chaos, Solitons & Fractals, Elsevier, vol. 28(5), pages 1204-1211.
    5. Chang, Wei-Der, 2006. "Parameter identification of Rossler’s chaotic system by an evolutionary algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1047-1053.
    6. Kousaka, Takuji & Ueta, Tetsushi & Ma, Yue & Kawakami, Hiroshi, 2006. "Control of chaos in a piecewise smooth nonlinear system," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 1019-1025.
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    Cited by:

    1. Zuñiga Aguilar, C.J. & Gómez-Aguilar, J.F. & Alvarado-Martínez, V.M. & Romero-Ugalde, H.M., 2020. "Fractional order neural networks for system identification," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    2. Shi, Xiancheng & Feng, Yucheng & Zeng, Jinsong & Chen, Kefu, 2017. "Chaos time-series prediction based on an improved recursive Levenberg–Marquardt algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 57-61.
    3. Mirzaee, Hossein, 2009. "Linear combination rule in genetic algorithm for optimization of finite impulse response neural network to predict natural chaotic time series," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2681-2689.
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    6. Banerjee, Amit & Abu-Mahfouz, Issam, 2014. "A comparative analysis of particle swarm optimization and differential evolution algorithms for parameter estimation in nonlinear dynamic systems," Chaos, Solitons & Fractals, Elsevier, vol. 58(C), pages 65-83.

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