Analytic Exact Upper Bound for the Lyapunov Dimension of the Shimizu–Morioka System
Leonov, G. A., Alexeeva, T. A., & Kuznetsov, N. (2015). Analytic Exact Upper Bound for the Lyapunov Dimension of the Shimizu–Morioka System. Entropy, 17(7), 5101-5116. https://doi.org/10.3390/e17075101
Julkaistu sarjassa
EntropyPäivämäärä
2015Tekijänoikeudet
© 2015 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article
distributed under the terms and conditions of the Creative Commons Attribution license
(http://creativecommons.org/licenses/by/4.0/).
In applied investigations, the invariance of the Lyapunov dimension under a diffeomorphism is often used. However, in the case of irregular linearization, this fact was not strictly considered in the classical works. In the present work, the invariance of the Lyapunov dimension under diffeomorphism is demonstrated in the general case. This fact is used to obtain the analytic exact upper bound of the Lyapunov dimension of an attractor of the Shimizu–Morioka system.
Julkaisija
MDPI AGISSN Hae Julkaisufoorumista
1099-4300Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/24867000
Metadata
Näytä kaikki kuvailutiedotKokoelmat
Lisenssi
Ellei muuten mainita, aineiston lisenssi on © 2015 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article
distributed under the terms and conditions of the Creative Commons Attribution license
(http://creativecommons.org/licenses/by/4.0/).
Samankaltainen aineisto
Näytetään aineistoja, joilla on samankaltainen nimeke tai asiasanat.
-
Lyapunov quantities and limit cycles in two-dimensional dynamical systems : analytical methods, symbolic computation and visualization
Kuznetsova, Olga (University of Jyväskylä, 2011) -
Localization and dimension estimation of attractors in the Glukhovsky-Dolzhansky system
Mokaev, Timur (University of Jyväskylä, 2016) -
Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system
Kuznetsov, Nikolay; Leonov, G. A.; Mokaev, T. N.; Prasad, A.; Shrimali, M. D. (Springer, 2018)The Rabinovich system, describing the process of interaction between waves in plasma, is considered. It is shown that the Rabinovich system can exhibit a hidden attractor in the case of multistability as well as a classical ... -
Lyapunov dimension formula for the global attractor of the Lorenz system
Leonov, G. A.; Kuznetsov, Nikolay; Korzhemanova, N. A.; Kusakin, D. V. (Elsevier B.V.; Peking University, 2016)The exact Lyapunov dimension formula for the Lorenz system for a positive measure set of parameters, including classical values, was analytically obtained first by G.A. Leonov in 2002. Leonov used the construction technique ... -
The Lorenz system : hidden boundary of practical stability and the Lyapunov dimension
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 ...
Ellei toisin mainittu, julkisesti saatavilla olevia JYX-metatietoja (poislukien tiivistelmät) saa vapaasti uudelleenkäyttää CC0-lisenssillä.