Hopf bifurcation and Si'lnikov chaos of Genesio system

被引：20

作者：

Zhou, Liangqiang ^{[1
,2
]}

Chen, Fangqi ^{[1
]}

机构：

[1] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 210016, Peoples R China

[2] Nanjing Univ Aeronaut & Astronaut, Dept Mech, Nanjing 210016, Peoples R China

来源：

CHAOS SOLITONS & FRACTALS | 2009年 / 40卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Nonlinear analysis;

D O I：

10.1016/j.chaos.2007.09.033

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Genesio system, which is a three-dimensional system with only one quadratic nonlinear term, is considered. It has two equilibrium points for some parameters. The Hopf bifurcation is discussed, and the existence of the homoclinic orbit for this system has been proven by using the undetermined coefficient method. As a result, the Si'lnikov criterion guarantees that the Genesio system has Smale horseshoe chaos. (C) 2007 Elsevier Ltd. All rights reserved.

引用

页码：1413 / 1422

页数：10

共 19 条

[1]

[Anonymous], 1998, ELEMENTS APPL BIFURC, DOI DOI 10.1007/B98848

[2]

Chen G., 1998, CHAOS ORDER METHODOL

[3]

CHEN G, 2003, DYNAMICS LORENZ FAMI

[4] Yet another chaotic attractor [J].

Chen, GR ;

Ueta, T .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1999, 9 (07) :1465-1466

[5] Controlling and synchronizing chaotic Genesio system via nonlinear feedback control [J].

Chen, MY ;

Han, ZZ .

CHAOS SOLITONS & FRACTALS, 2003, 17 (04) :709-716

[6] HARMONIC-BALANCE METHODS FOR THE ANALYSIS OF CHAOTIC DYNAMICS IN NONLINEAR-SYSTEMS [J].

GENESIO, R ;

TESI, A .

AUTOMATICA, 1992, 28 (03) :531-548

[7] Si'lnikov homoclinic orbits in a new chaotic system [J].

Jiang, Yongxin ;

Sun, Jianhua .

CHAOS SOLITONS & FRACTALS, 2007, 32 (01) :150-159

[8]

JU H, 2007, CHAOS SOLITON FRACT, V34, P1154

[9]

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

[10]

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