Amplitude control of limit cycles in Langford system

被引：15

作者：

Cui, Yan ^{[1
,2
]}

Liu, Suhua ^{[1
,3
]}

Tang, Jiashi ^{[3
]}

Meng, Yimin ^{[4
]}

机构：

[1] Shanghai Univ Engn Sci, Vocat Tech Coll, Shanghai 200437, Peoples R China

[2] E China Univ Sci & Technol, Sch Mech & Power Engn, Shanghai 200237, Peoples R China

[3] Hunan Univ, Coll Mech & Aerosp, Changsha 410082, Hunan, Peoples R China

[4] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China

来源：

CHAOS SOLITONS & FRACTALS | 2009年 / 42卷 / 01期

关键词：

LINEAR FEEDBACK-CONTROL; BIFURCATION CONTROL; HOPF BIFURCATIONS; TIME-SYSTEMS;

D O I：

10.1016/j.chaos.2008.12.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we investigate the control of amplitude of limit cycle emerging from the Hopf bifurcation in Langford system under a nonlinear feedback controller. Explicit nonlinear control formulae and amplitude approximations in terms of control gains are derived from the center manifold theory and normal form reduction. The formulae and expressions for the Langford system present a convenient approach to obtain an effective analytical control and predict the amplitude of limit cycles in this system. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：335 / 340

页数：6

共 17 条

[1] LOCAL FEEDBACK STABILIZATION AND BIFURCATION CONTROL .1. HOPF-BIFURCATION [J].

ABED, EH ;

FU, JH .

SYSTEMS & CONTROL LETTERS, 1986, 7 (01) :11-17

[2] An amplitude-phase formulation for nonlinear modes and limit cycles through invariant manifolds [J].

Bellizzi, S. ;

Bouc, R. .

JOURNAL OF SOUND AND VIBRATION, 2007, 300 (3-5) :896-915

[3] Bifurcation control: Theories, methods, and applications [J].

Chen, GR ;

Moiola, JL ;

Wang, HO .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2000, 10 (03) :511-548

[4]

Hassard BD, 1981, THEORY APPL HOPF BIF

[5] A MATHEMATICAL EXAMPLE DISPLAYING FEATURES OF TURBULENCE [J].

HOPF, E .

COMMUNICATIONS ON APPLIED MATHEMATICS, 1948, 1 (04) :303-322

[6] Linear feedback control of Hopf bifurcation in Langford system [J].

Liu Su-Hua ;

Tang Jia-Shi .

ACTA PHYSICA SINICA, 2007, 56 (06) :3145-3151

[7]

Moiola JL, 1997, IEEE DECIS CONTR P, P1479, DOI 10.1109/CDC.1997.657675

[8] Bifurcations in a power system model [J].

Nayfeh, AH ;

Harb, AM ;

Chin, CM .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1996, 6 (03) :497-512

[9] Bifurcations and chaotic behavior on the Lanford system [J].

Nikolov, S ;

Bozhkov, B .

CHAOS SOLITONS & FRACTALS, 2004, 21 (04) :803-808

[10] Single-mode control of a cantilever beam under principal parametric excitation [J].

Oueini, SS ;

Nayfeh, AH .

JOURNAL OF SOUND AND VIBRATION, 1999, 224 (01) :33-47

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