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Identifying chaotic systems using a fuzzy model coupled with a linear plant

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  • Yeh, Jiin-Po

Abstract

In this paper, a model for identifying chaotic systems is derived from the theory of a feed-forward neural network with three layers. One part of the derived model has the form of a fuzzy logic-based intelligent mechanism; the other part is a linear difference equation, similar to the Wiener-type cascade structure. Three dynamical systems are presented to demonstrate the effectiveness of the proposed model: a one-dimensional logistic map, two-dimensional Hénon map and the continuous-time pendulum system. For both discrete-time and continuous-time chaotic systems, the proposed model always takes the form of a difference equation. Numerical simulations show that the proposed model can well identify the dynamical systems. Time series and time-delayed pseudo-phase plane plots are drawn for both the dynamical systems and the proposed model.

Suggested Citation

  • Yeh, Jiin-Po, 2007. "Identifying chaotic systems using a fuzzy model coupled with a linear plant," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 1178-1187.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:3:p:1178-1187
    DOI: 10.1016/j.chaos.2005.11.087
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    References listed on IDEAS

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    1. de Oliveira, Kenya Andrésia & Vannucci, Álvaro & da Silva, Elton Cesar, 2000. "Using artificial neural networks to forecast chaotic time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 393-404.
    2. Ge, Zheng-Ming & Lee, Ching-I, 2005. "Control, anticontrol and synchronization of chaos for an autonomous rotational machine system with time-delay," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1855-1864.
    3. Alasty, Aria & Salarieh, Hassan, 2005. "Controlling the chaos using fuzzy estimation of OGY and Pyragas controllers," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 379-392.
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    Cited by:

    1. Sangiorgio, Matteo & Dercole, Fabio, 2020. "Robustness of LSTM neural networks for multi-step forecasting of chaotic time series," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Coelho, Leandro dos Santos & Araujo, Ernesto, 2009. "Identification of the Hénon chaotic map by fuzzy modeling and Nelder–Mead simplex method," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2762-2772.
    3. Cao, Weijia & Cai, Hang & Hua, Zhongyun, 2022. "n-Dimensional Chaotic Map with application in secure communication," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).

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