Numerical justification of Leonov conjecture on Lyapunov dimension of Rossler attractor

被引：93

作者：

Kuznetsov, N. V. ^{[1
,2
]}

Mokaev, T. N. ^{[1
]}

Vasilyev, P. A. ^{[1
]}

机构：

[1] St Petersburg State Univ, Math & Mech Fac, St Petersburg 198504, Russia

[2] Univ Jyvaskyla, Dept Math Informat Technol, Jyvaskyla 40014, Finland

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2014年 / 19卷 / 04期

基金：

俄罗斯基础研究基金会; 芬兰科学院;

关键词：

Rssler system; Lyapunov dimension; Strange attractor; Lyapunov exponent; Chaos; Leonov's conjecture; INVARIANT-SETS; FRACTAL DIMENSION; BIFURCATIONS; HAUSDORFF; EQUATIONS;

D O I：

10.1016/j.cnsns.2013.07.026

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Exact Lyapunov dimension of attractors of many classical chaotic systems (such as Lorenz, Henon, and Chirikov systems) is obtained. While exact Lyapunov dimension for Rssler system is not known, Leonov formulated the following conjecture: Lyapunov dimension of Rssler attractor is equal to local Lyapunov dimension in one of its stationary points. In the present work Leonov's conjecture on Lyapunov dimension of various Rssler systems with standard parameters is checked numerically. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：1027 / 1034

页数：8

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