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Sensitivity tools vs. Poincaré sections

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  • Barrio, Roberto

Abstract

In this paper we introduce a modification of the fast Lyapunov indicator (FLI) denominated OFLITT2 indicator that may provide a global picture of the evolution of a dynamical system. Therefore, it gives an alternative or a complement to the pictures given by the classical Poincaré sections and, besides, it may be used for any dimension. We present several examples comparing with the Poincaré sections in two classical problems, the Hénon–Heiles and the extensible-pendulum problems. Besides, we show the application to Hamiltonians of three degrees of freedom as an isotropic harmonic oscillator in three dimensions perturbed by a cubic potential and non-Hamiltonian problems as a four-dimensional chaotic system. Finally, a numerical method especially designed for its computation is presented in the appendix.

Suggested Citation

  • Barrio, Roberto, 2005. "Sensitivity tools vs. Poincaré sections," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 711-726.
    • Handle: RePEc:eee:chsofr:v:25:y:2005:i:3:p:711-726
    DOI: 10.1016/j.chaos.2004.11.092
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    1. Qi, Guoyuan & Du, Shengzhi & Chen, Guanrong & Chen, Zengqiang & yuan, Zhuzhi, 2005. "On a four-dimensional chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1671-1682.
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    Cited by:

    1. Ghanbari, Behzad, 2021. "On detecting chaos in a prey-predator model with prey’s counter-attack on juvenile predators," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    2. Zarouan, Mohamed & Allali, Sofiène & Benrejeb, Mohamed, 2009. "Correlation between the bifurcation diagram structure and the predominant harmonics of an electrical power network response," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 483-491.
    3. Barrio, R. & Borczyk, W. & Breiter, S., 2009. "Spurious structures in chaos indicators maps," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1697-1714.
    4. Barrio, Roberto & Blesa, Fernando, 2009. "Systematic search of symmetric periodic orbits in 2DOF Hamiltonian systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 560-582.
    5. Barrio, Roberto & Blesa, Fernando & Serrano, Sergio, 2008. "Qualitative analysis of the (N+1)-body ring problem," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 1067-1088.
    6. Canbaz, Beyrul, 2022. "Chaos classification in forced fermionic instanton solutions by the Generalized Alignment Index (GALI) and the largest Lyapunov exponent," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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