A1 Journal article (refereed)
The Lorenz system : hidden boundary of practical stability and the Lyapunov dimension (2020)
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
JYU authors or editors
Publication details
All authors or editors: Kuznetsov, N. V.; Mokaev, T. N.; Kuznetsova, O. A.; Kudryashova, E. V.
Journal or series: Nonlinear Dynamics
ISSN: 0924-090X
eISSN: 1573-269X
Publication year: 2020
Publication date: 11/08/2020
Volume: 102
Issue number: 2
Pages range: 713-732
Publisher: Springer
Publication country: Netherlands
Publication language: English
DOI: https://doi.org/10.1007/s11071-020-05856-4
Publication open access: Openly available
Publication channel open access: Partially open access channel
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/71406
Abstract
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.
Keywords: dynamical systems; attractors; chaos theory; control theory; numerical analysis
Free keywords: global stability; chaos; hidden attractor; transient set; Lyapunov exponents; Lyapunov dimension; unstable periodic orbit; time-delayed feedback control
Contributing organizations
Ministry reporting: Yes
Reporting Year: 2020
JUFO rating: 2