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

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


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

Last updated on 2021-17-09 at 16:41