Si'lnikov homoclinic orbits in a new chaotic system

被引：32

作者：

Jiang, Yongxin ^{[1
]}

Sun, Jianhua ^{[1
]}

机构：

[1] Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China

来源：

CHAOS SOLITONS & FRACTALS | 2007年 / 32卷 / 01期

基金：

中国国家自然科学基金;

关键词：

D O I：

10.1016/j.chaos.2005.10.088

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the present paper, a new chaotic system is considered, which is a three-dimensional quadratic system and exhibits two 1-scroll chaotic attractors simultaneously with only three equilibria for some parameters. The existence of Si'lnikov homoclinic orbits in this system has been proven by using the undetermined coefficient method. As a result, the Si'lnikov criterion guarantees that the system has Smale horseshoes. Moreover, the geometric structures of attractors are determined by these homoclinic orbits. (c) 2005 Elsevier Ltd. All rights reserved.

引用

页码：150 / 159

页数：10

共 14 条

[1]

[Anonymous], 2002, CHAOTIC TIME SERIES

[2]

Chen G., 1998, CHAOS ORDER METHODOL

[3] A new chaotic system and its generation [J].

Liu, WB ;

Chen, GR .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2003, 13 (01) :261-267

[4] Can a three-dimensional smooth autonomous quadratic chaotic system generate a single four-scroll attractor? [J].

Liu, WB ;

Chen, GR .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2004, 14 (04) :1395-1403

[5] A new chaotic system and beyond:: The generalized Lorenz-like system [J].

Lü, JH ;

Chen, GR ;

Cheng, DZ .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2004, 14 (05) :1507-1537

[6]

SILNIKOV LP, 1965, SOV MATH DOKL, V6, P163

[7]

SILNIKOV LP, 1970, MATH USSR SB, V10, P91, DOI DOI 10.1070/SM1970V010N01ABEH001588

[8] SHILNIKOV THEOREM - A TUTORIAL [J].

SILVA, CP .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS, 1993, 40 (10) :675-682

[9]

Wiggins S., 1988, GLOBAL BIFURCATION C

[10]

ZHENG Z, EXISTENCE HETEROCLIN

← 1 2 →