The basin of attraction of the Liu system

被引：17

作者：

Liu, Yongjian ^{[1
,2
]}

Pang, Guoping ^{[2
]}

机构：

[1] S China Univ Technol, Sch Math Sci, Guangzhou 510640, Guangdong, Peoples R China

[2] Yulin Normal Univ, Dept Math & Computat Sci, Yulin 537000, Peoples R China

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2011年 / 16卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Liu system; Chaotic attractor; Basin of attraction; Riddled property; Milnor strange attractor; CHAOS CONTROL; SYNCHRONIZATION; DISCRETE;

D O I：

10.1016/j.cnsns.2010.08.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By geometric analysis the riddled property of the basin of attraction of the Liu attractor is discussed and that any neighborhood of the Liu attractor contains repelled sets with positive Lebesgue measures is proved Based on mathematical analytic and numerical results it is shown that the Liu attractor indeed has some unusual properties leading to a strange attractor in the sense of Milnor (C) 2010 Elsevier B V All rights reserved

引用

页码：2065 / 2071

页数：7

共 20 条

[11]

LORENZ EN, 1963, J ATMOS SCI, V20, P130, DOI 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO

[12]

[13] A new chaotic attractor coined [J].

Lü, JH ;

Chen, GR .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2002, 12 (03) :659-661

[14] ON THE CONCEPT OF ATTRACTOR [J].

MILNOR, J .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1985, 99 (02) :177-195

[15] THE TRANSITION TO CHAOTIC ATTRACTORS WITH RIDDLED BASINS [J].

OTT, E ;

ALEXANDER, JC ;

KAN, I ;

SOMMERER, JC ;

YORKE, JA .

PHYSICA D, 1994, 76 (04) :384-410

[16] EQUATION FOR CONTINUOUS CHAOS [J].

ROSSLER, OE .

PHYSICS LETTERS A, 1976, 57 (05) :397-398

[17] On the structure of attractors for discrete, periodically forced systems with applications to population models [J].

Selgrade, JF ;

Roberds, JH .

PHYSICA D, 2001, 158 (1-4) :69-82

[18]

Sparrow C., 1982, The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors

[19] Analysis for the stabilization of impulsive control Liu's system [J].

Xu, Wei ;

Wang, Liang ;

Rong, Haiwu ;

Li, Dongxi ;

Niu, Yujun .

CHAOS SOLITONS & FRACTALS, 2009, 42 (02) :1143-1148

[20] Hopf bifurcation analysis of the Liu system [J].

Zhou, Xiaobing ;

Wu, Yue ;

Li, Yi ;

Wei, Zhengxi .

CHAOS SOLITONS & FRACTALS, 2008, 36 (05) :1385-1391

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