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
Published inJournal of Physics: Conference Series
© 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.
ConferenceInternational Conference Problems of Mathematical Physics and Mathematical Modelling
Is part of publicationMPMM 2018 : VII International Conference Problems of Mathematical Physics and Mathematical Modelling
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Kuznetsov, N. V.; Mokaev, T. N.; Kuznetsova, O. A.; Kudryashova, E. V. (Springer, 2020)On the example of the famous Lorenz system, the difficulties and opportunities of reliable numerical analysis of chaotic dynamical systems are discussed in this article. For the Lorenz system, the boundaries of global ...
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Mokaev, Timur (University of Jyväskylä, 2016)
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