Numerical analysis of dynamical systems : unstable periodic orbits, hidden transient chaotic sets, hidden attractors, and finite-time Lyapunov dimension
Kuznetsov, N., & Mokaev, T. (2019). Numerical analysis of dynamical systems : unstable periodic orbits, hidden transient chaotic sets, hidden attractors, and finite-time Lyapunov dimension. In V. V. Kozlov, N. A. Kudryashov, & O. V. Nagornov (Eds.), MPMM 2018 : VII International Conference Problems of Mathematical Physics and Mathematical Modelling (Article 012034). IOP Publishing. Journal of Physics: Conference Series, 1205. https://doi.org/10.1088/1742-6596/1205/1/012034
Julkaistu sarjassa
Journal of Physics: Conference SeriesPäivämäärä
2019Tekijänoikeudet
© IOP Publishing Limited, 2019.
In this article, on the example of the known low-order dynamical models, namely Lorenz, Rössler and Vallis systems, the difficulties of reliable numerical analysis of chaotic dynamical systems are discussed. For the Lorenz system, the problems of existence of hidden chaotic attractors and hidden transient chaotic sets and their numerical investigation are considered. The problems of the numerical characterization of a chaotic attractor by calculating finite-time time Lyapunov exponents and finite-time Lyapunov dimension along one trajectory are demonstrated using the example of computing unstable periodic orbits in the Rössler system. Using the example of the Vallis system describing the El Ninõ-Southern Oscillation it is demonstrated an analytical approach for localization of self-excited and hidden attractors, which allows to obtain the exact formulas or estimates of their Lyapunov dimensions.
Julkaisija
IOP PublishingKonferenssi
International Conference Problems of Mathematical Physics and Mathematical ModellingKuuluu julkaisuun
MPMM 2018 : VII International Conference Problems of Mathematical Physics and Mathematical ModellingISSN Hae Julkaisufoorumista
1742-6588Asiasanat
Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/30677409
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