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- W3048600509 endingPage "732" @default.
- W3048600509 startingPage "713" @default.
- W3048600509 abstract "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." @default.
- W3048600509 created "2020-08-18" @default.
- W3048600509 creator A5018839299 @default.
- W3048600509 creator A5021204100 @default.
- W3048600509 creator A5066641811 @default.
- W3048600509 creator A5088627239 @default.
- W3048600509 date "2020-08-11" @default.
- W3048600509 modified "2023-10-01" @default.
- W3048600509 title "The Lorenz system: hidden boundary of practical stability and the Lyapunov dimension" @default.
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- W3048600509 doi "https://doi.org/10.1007/s11071-020-05856-4" @default.