2020/08/11 by Н. В. Кузнецов, T. N. Mokaev, О. А. Кузнецова +1 · 1 citation
Physics and Astronomy · Computer Science · Mathematics · #Chaos control and synchronization #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #Attractor #Lorenz system #Lyapunov function #Mathematics #Lyapunov exponent #Context (archaeology) #Dimension (graph theory) #Chaotic #Stability (learning theory) #Boundary (topology) #Computation #Applied mathematics #Dynamical systems theory #Control theory (sociology) #Mathematical analysis #Computer science #Nonlinear system #Physics #Control (management) #Algorithm
paper · pdf · doi:10.1007/s11071-020-05856-4
openalex publication_date 2020/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
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.