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A smooth-piecewise model to the Cord Attractor

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  • Amaral, Gleison F.V.
  • Nepomuceno, Erivelton G.

Abstract

This paper reports a smooth-piecewise model to the Cord Attractor. The fact that the Cord Attractor has one real fixed point and two complex conjugate fixed points does not allow to use a technique based on the building of two affine subsystems, which requires at least two real fixed points [Chaos 16, 013115 (2006)]. In this work, we have presented a procedure to at least partially overcome this limitation using a virtual fixed point; the location of the fixed point is based on the topology of the original system. The switching function has been designed as a smooth function. The phase space and the local-finite largest Lyapunov exponent have been used to compare the resulting attractor with the original Cord Attractor.

Suggested Citation

  • Amaral, Gleison F.V. & Nepomuceno, Erivelton G., 2018. "A smooth-piecewise model to the Cord Attractor," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 31-35.
    • Handle: RePEc:eee:chsofr:v:109:y:2018:i:c:p:31-35
    DOI: 10.1016/j.chaos.2018.02.001
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    References listed on IDEAS

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    1. Nepomuceno, Erivelton Geraldo & Mendes, Eduardo M.A.M., 2017. "On the analysis of pseudo-orbits of continuous chaotic nonlinear systems simulated using discretization schemes in a digital computer," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 21-32.
    2. Ramos, J.I., 2006. "Determination of periodic orbits of nonlinear oscillators by means of piecewise-linearization methods," Chaos, Solitons & Fractals, Elsevier, vol. 28(5), pages 1306-1313.
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    Cited by:

    1. Mahmoodi, Kumars & Nepomuceno, Erivelton & Razminia, Abolhassan, 2022. "Wave excitation force forecasting using neural networks," Energy, Elsevier, vol. 247(C).

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