Russian Physics Journal

, Volume 60, Issue 10, pp 1728–1738 | Cite as

Second-Order Chaos Indicators MEGNO2 and OMEGNO2: Theory

Article

Modifications of the Mean Exponential Growth factor of Nearby Orbits (MEGNO) linear variational method called MEGNO2 and OMEGNO2 indicators are introduced. The modifications are based on taking into account not only the linear, but also the nonlinear part of the increment of the phase flow in the divergence among nearby trajectories according to the second-order formulas. The new indicators allow one to determine more quickly the nature of the orbits under study in dynamical systems with zero or small Lyapunov exponents in comparison with the first-order variational indicators. They improve the analysis of regular regions and, in particular, periodic orbits as well as prevent the appearance of spurious structures in the resulting mappings.

Keywords

regular and chaotic dynamics variational chaos indicators MEGNO method 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.National Research Tomsk State UniversityTomskRussia

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