The Lu system is a particular case of the Lorenz system

被引：30

作者：

Algaba, Antonio ^{[1
]}

Fernandez-Sanchez, Fernando ^{[2
]}

Merino, Manuel ^{[1
]}

Rodriguez-Luis, Alejandro J. ^{[2
]}

机构：

[1] Univ Huelva, Dept Matemat, Ctr Invest Fis Teor & Matemat FIMAT, Huelva 21071, Spain

[2] Univ Seville, Dept Matemat Aplicada 2, ETS Ingn, Seville 41092, Spain

来源：

PHYSICS LETTERS A | 2013年 / 377卷 / 39期

关键词：

Lorenz system; Lu system; Local bifurcation; Periodic orbit; Invariant algebraic surface; Chaotic attractor; CODIMENSION-2 BAUTIN BIFURCATION; INVARIANT ALGEBRAIC-SURFACES; SILNIKOV-TYPE ORBITS; CHAOTIC SYSTEM; HETEROCLINIC ORBITS; HOPF-BIFURCATION; ADAPTIVE SYNCHRONIZATION; GLOBAL DYNAMICS; SHILNIKOV TYPE; ATTRACTOR;

D O I：

10.1016/j.physleta.2013.08.034

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Between the so-called Lorenz-like systems, the Lu system, <(x)over dot> = a(y - x), <(y)over dot> = cy - xz, <(z)over dot> = -bz + xy, has attracted great interest in the last decade. In this Letter we show that, generically (c not equal 0), there is a homothetic transformation which converts the Lu system into the Lorenz system and, therefore, all the dynamical behavior exhibited by the Lu system is also present in the Lorenz system. Consequently, all the results obtained in the papers devoted to the study of the Lu system can be trivially derived from the corresponding results on the Lorenz system. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：2771 / 2776

页数：6

共 92 条

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[2]

Algaba A., 2006, J MATH ANAL AP UNPUB, V323, P844

[3] Comments on 'Global dynamics of the generalized Lorenz systems having invariant algebraic surfaces' [J].

Algaba, Antonio ;

Fernandez-Sanchez, Fernando ;

Merino, Manuel ;