2015/08/29 by Г. А. Леонов, G. A. Leonov, Н. В. Кузнецов +3 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Applied mathematics #Attractor #Chaos control and synchronization #Dimension (graph theory) #Lorenz system #Lyapunov function #Mathematical analysis #Mathematics #Nonlinear Dynamics and Pattern Formation #Nonlinear system #Physics #Pure mathematics #Quantum chaos and dynamical systems #Rössler attractor #math.DS #nlin.CD
paper · pdf · doi:10.1016/j.cnsns.2016.04.032
arXiv admin note: text overlap with arXiv:1505.04729
arxiv created 2015/08/29 · openalex publication_date 2016/05/01 · arxiv updated 2016/06/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The exact Lyapunov dimension formula for the Lorenz system has been analytically obtained first due to G.A.Leonov in 2002 under certain restrictions on parameters, permitting classical values. He used the construction technique of special Lyapunov-type functions developed by him in 1991 year. Later it was shown that the consideration of larger class of Lyapunov-type functions permits proving the validity of this formula for all parameters of the system such that all the equilibria of the system are hyperbolically unstable. In the present work it is proved the validity of the formula for Lyapunov dimension for a wider variety of parameters values, which include all parameters satisfying the classical physical limitations. One of the motivation of this work is the possibility of computing a chaotic attractor in the Lorenz system in the case of one unstable and two stable equilibria.