The Lorenz system: hidden boundary of practical stability and the Lyapunov dimension
The Lorenz system: hidden boundary of practical stability and the Lyapunov dimension
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DOI：
10.1007/s11071-020-05856-4
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发表时间：
2020-08-11
影响因子：
5.6
通讯作者：
Kudryashova, E., V
中科院分区：
文献类型：
--
作者：
Kuznetsov, N., V;Mokaev, T. N.;Kudryashova, E., V
以著名的Lorenz系统为例，讨论了混沌动力系统可靠数值分析的困难和机遇。对于Lorenz系统，估计了系统的全局稳定性边界，讨论了由于全局稳定性的丧失而导致的自激吸引子和隐吸引子的产生.讨论了大时间间隔内沿轨道沿着有限时间李雅普诺夫维数的可靠数值计算问题。通过Pyragas时间延迟反馈控制技术和Leonov方法估计吸引子的Lyapunov维数。考虑到可靠的数值实验中的阴影和双曲理论的背景下，实验进行小的时间间隔和初始点的吸引子的吸引力盆地的网格上的轨迹。
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.