On differences and similarities in the analysis of Lorenz, Chen, and Lu systems

被引：108

作者：

Leonov, G. A.

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

机构：

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

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2015年 / 256卷

基金：

俄罗斯科学基金会;

关键词：

Lorenz-like systems; Lorenz system; Chen system; Lu system; Lyapunov exponent; Chaotic analog of 16th Hilbert problem; INVARIANT ALGEBRAIC-SURFACES; HAUSDORFF DIMENSION; LYAPUNOV DIMENSION; HIDDEN ATTRACTORS; HOMOCLINIC ORBITS; EXISTENCE; BIFURCATION; DYNAMICS; MODEL;

D O I：

10.1016/j.amc.2014.12.132

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Currently it is being actively discussed the question of the equivalence of various Lorenz-like systems and the possibility of universal consideration of their behavior (Algaba et al., 2013a, b, 2014b, c; Chen, 2013; Chen and Yang, 2013; Leonov, 2013a), in view of the possibility of reduction of such systems to the same form with the help of various transformations. In the present paper the differences and similarities in the analysis of the Lorenz, the Chen and the Lu systems are discussed. It is shown that the Chen and the Lu systems stimulate the development of new methods for the analysis of chaotic systems. Open problems are discussed. (C) 2015 The Authors. Published by Elsevier Inc.

引用

页码：334 / 343

页数：10

共 83 条

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