Bifurcation control for a non-autonomous system with two time delays

被引：18

作者：

Qian, CZ ^{[1
]}

Tang, JS

机构：

[1] Hunan Univ, Dept Mech, Changsha 410082, Peoples R China

[2] Changsha Univ Sci & Technol, Coll Bridge & Struct Engn, Changsha 410076, Peoples R China

来源：

ACTA PHYSICA SINICA | 2006年 / 55卷 / 02期

关键词：

perturbation method; bifurcation control; dynamics of nonlinear systems involving time delays;

D O I：

10.7498/aps.55.617

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A forced system with two time-delays, including van der Pol-Duffing types, is studied. The aim is to study the primary parametrical resonance bifurcation of this system. Perturbation method is used to obtain the bifurcation equation with time-delays. Based on the bifurcation equation, co-dimension one, co-dimension two and Hope bifurcation are discussed, and the effect of time-delays on the steady state response is analyzed by numerical methods. It is indicated that the primary resonance bifurcation can be well controlled by time-delays feedback.

引用

页码：617 / 621

页数：5

共 18 条

[1] Bifurcations and chaos in a linear control system with saturated input [J].

Alvarez, J ;

Curiel, LE .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1997, 7 (08) :1811-1822

[2]

ATTILIO M, 2003, INT J NONLIN MECH, V38, P123

[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] Superharmonic resonance bifurcation control of parametrically excited system based on state feedback strategy [J].

Fu, WB ;

Tang, JS .

ACTA PHYSICA SINICA, 2004, 53 (09) :2889-2893

[5]

Hu H., 1999, Advances in Mechanics, V29, P501

[6] Stability analysis of damped SDOF systems with two time delays in state feedback [J].

Hu, HY ;

Wang, ZH .

JOURNAL OF SOUND AND VIBRATION, 1998, 214 (02) :213-225

[7]

JI CJ, 2002, INT J SOUND VIB, V253, P985

[8] Mechanism of time-delayed feedback control [J].

Just, W ;

Bernard, T ;

Ostheimer, M ;

Reibold, E ;

Benner, H .

PHYSICAL REVIEW LETTERS, 1997, 78 (02) :203-206

[9] Analysis of static and dynamic bifurcations from a feedback systems perspective [J].

Moiola, JL ;

Colantonio, MC ;

Donate, PD .

DYNAMICS AND STABILITY OF SYSTEMS, 1997, 12 (04) :293-317

[10]

NAYFEH AH, 1978, NONLINEAR OSCILLATIO, P61

← 1 2 →