The Lorenz system : hidden boundary of practical stability and the Lyapunov dimension
Kuznetsov, N. V., Mokaev, T. N., Kuznetsova, O. A., & Kudryashova, E. V. (2020). The Lorenz system : hidden boundary of practical stability and the Lyapunov dimension. Nonlinear Dynamics, 102(2), 713-732. https://doi.org/10.1007/s11071-020-05856-4
Julkaistu sarjassa
Nonlinear DynamicsPäivämäärä
2020Tekijänoikeudet
© 2020 the Authors
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 stability are estimated and the difficulties of numerically studying the birth of self-excited and hidden attractors, caused by the loss of global stability, are discussed. The problem of reliable numerical computation of the finite-time Lyapunov dimension along the trajectories over large time intervals is discussed. Estimating the Lyapunov dimension of attractors via the Pyragas time-delayed feedback control technique and the Leonov method is demonstrated. Taking into account the problems of reliable numerical experiments in the context of the shadowing and hyperbolicity theories, experiments are carried out on small time intervals and for trajectories on a grid of initial points in the attractor’s basin of attraction.
Julkaisija
SpringerISSN Hae Julkaisufoorumista
0924-090XAsiasanat
Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/41733182
Metadata
Näytä kaikki kuvailutiedotKokoelmat
Lisätietoja rahoituksesta
Open access funding provided by University of Jyväskylä (JYU). This study was partially funded by the Russian Science Foundation (Project 19-41-02002).Lisenssi
Samankaltainen aineisto
Näytetään aineistoja, joilla on samankaltainen nimeke tai asiasanat.
-
Numerical analysis of dynamical systems : unstable periodic orbits, hidden transient chaotic sets, hidden attractors, and finite-time Lyapunov dimension
Kuznetsov, Nikolay; Mokaev, Timur (IOP Publishing, 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 ... -
D3 Dihedral Logistic Map of Fractional Order
Danca, Marius-F.; Kuznetsov, Nikolay (MDPI AG, 2022)In this paper, the D3 dihedral logistic map of fractional order is introduced. The map presents a dihedral symmetry D3. It is numerically shown that the construction and interpretation of the bifurcation diagram versus the ... -
Complex dynamics, hidden attractors and continuous approximation of a fractional-order hyperchaotic PWC system
Danca, Marius-F.; Fečkan, Michal; Kuznetsov, Nikolay; Chen, Guanrong (Springer, 2018) -
Hidden Strange Nonchaotic Attractors
Danca, Marius-F.; Kuznetsov, Nikolay (MDPI AG, 2021)In this paper, it is found numerically that the previously found hidden chaotic attractors of the Rabinovich–Fabrikant system actually present the characteristics of strange nonchaotic attractors. For a range of the ... -
Hidden attractors in Chua circuit : mathematical theory meets physical experiments
Kuznetsov, Nikolay; Mokaev, Timur; Ponomarenko, Vladimir; Seleznev, Evgeniy; Stankevich, Nataliya; Chua, Leon (Springer Science and Business Media LLC, 2023)After the discovery in early 1960s by E. Lorenz and Y. Ueda of the first example of a chaotic attractor in numerical simulation of a real physical process, a new scientific direction of analysis of chaotic behavior in ...
Ellei toisin mainittu, julkisesti saatavilla olevia JYX-metatietoja (poislukien tiivistelmät) saa vapaasti uudelleenkäyttää CC0-lisenssillä.