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Spurious structures in chaos indicators maps

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  • Barrio, R.
  • Borczyk, W.
  • Breiter, S.

Abstract

The paper confronts chaos indicators of two basic types: spectral methods and variational methods. The spectral methods include the spectral numbers and the integrated autocorrelation function. Variational methods discussed are FLI, MEGNO and OFLI2. Using an ad hoc model of coupled pendulum we demonstrate various spurious patterns that appear in the maps of the chaos indicators. Spectral methods generate spurious Moiré fringes, whereas variational methods are sensitive to the integration time or – in the case of the first-order variations indicators – to the initial direction of the variations vector. An example of major discrepancy between the two kinds of methods is given for an unstable periodic orbit. The influence of the initial variations vector is explained in the context of Lyapunov vectors theory and some selection rules are recommended.

Suggested Citation

  • Barrio, R. & Borczyk, W. & Breiter, S., 2009. "Spurious structures in chaos indicators maps," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1697-1714.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:4:p:1697-1714
    DOI: 10.1016/j.chaos.2007.09.084
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    References listed on IDEAS

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    1. Barrio, Roberto, 2005. "Sensitivity tools vs. Poincaré sections," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 711-726.
    2. Buszko, Katarzyna & Stefański, Krzysztof, 2006. "Measuring transient chaos in nonlinear one- and two-dimensional maps," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 630-646.
    3. Bashkirtseva, Irina & Ryashko, Lev, 2005. "Sensitivity and chaos control for the forced nonlinear oscillations," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1437-1451.
    4. 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.
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