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A multiparameter chaos control method based on OGY approach

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  • de Paula, Aline Souza
  • Savi, Marcelo Amorim

Abstract

Chaos control is based on the richness of responses of chaotic behavior and may be understood as the use of tiny perturbations for the stabilization of a UPO embedded in a chaotic attractor. Since one of these UPO can provide better performance than others in a particular situation the use of chaos control can make this kind of behavior to be desirable in a variety of applications. The OGY method is a discrete technique that considers small perturbations promoted in the neighborhood of the desired orbit when the trajectory crosses a specific surface, such as a Poincaré section. This contribution proposes a multiparameter semi-continuous method based on OGY approach in order to control chaotic behavior. Two different approaches are possible with this method: coupled approach, where all control parameters influences system dynamics although they are not active; and uncoupled approach that is a particular case where control parameters return to the reference value when they become passive parameters. As an application of the general formulation, it is investigated a two-parameter actuation of a nonlinear pendulum control employing coupled and uncoupled approaches. Analyses are carried out considering signals that are generated by numerical integration of the mathematical model using experimentally identified parameters. Results show that the procedure can be a good alternative for chaos control since it provides a more effective UPO stabilization than the classical single-parameter approach.

Suggested Citation

  • de Paula, Aline Souza & Savi, Marcelo Amorim, 2009. "A multiparameter chaos control method based on OGY approach," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1376-1390.
  • Handle: RePEc:eee:chsofr:v:40:y:2009:i:3:p:1376-1390
    DOI: 10.1016/j.chaos.2007.09.056
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    Cited by:

    1. Gois, Sandra R.F.S.M. & Savi, Marcelo A., 2009. "An analysis of heart rhythm dynamics using a three-coupled oscillator model," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2553-2565.
    2. de Paula, Aline Souza & Savi, Marcelo Amorim, 2009. "Controlling chaos in a nonlinear pendulum using an extended time-delayed feedback control method," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2981-2988.
    3. García, P., 2022. "A machine learning based control of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    4. Boukabou, Abdelkrim & Mekircha, Naim, 2012. "Generalized chaos control and synchronization by nonlinear high-order approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(11), pages 2268-2281.
    5. Ferreira, Bianca Borem & de Paula, Aline Souza & Savi, Marcelo Amorim, 2011. "Chaos control applied to heart rhythm dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 44(8), pages 587-599.
    6. Gritli, Hassène, 2019. "Poincaré maps design for the stabilization of limit cycles in non-autonomous nonlinear systems via time-piecewise-constant feedback controllers with application to the chaotic Duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 127-145.

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