DUFFING-VAN DER POL-TYPE OSCILLATOR SYSTEM AND ITS FIRST INTEGRALS

被引：9

作者：

Feng, Zhaosheng ^{[1
]}

Gao, Guangyue ^{[1
]}

Cui, Jing ^{[1
]}

机构：

[1] Univ Texas Pan Amer, Dept Math, Edinburg, TX 78539 USA

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2011年 / 10卷 / 05期

关键词：

First integral; Duffing oscillator; van der Pol oscillator; diffeomorphism; Lie symmetry method; Lie point symmetry; prolonged infinitesimal operator; parametric solution; ORDINARY DIFFERENTIAL-EQUATIONS; DE-VRIES EQUATION; HELMHOLTZ OSCILLATOR; INTEGRABILITY; SYMMETRIES;

D O I：

10.3934/cpaa.2011.10.1377

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, under certain parametric conditions we are concerned with the first integrals of the Duffing-van der Pol-type oscillator system, which include the van der Pol oscillator and the damped Duffing oscillator etc as particular cases. We apply the Lie symmetry method to find two nontrivial infinitesimal generators and use them to construct canonical variables. Through the inverse transformations we obtain the first integrals of the original oscillator system under the given parametric conditions, and some particular cases such as the damped Duffing equation and the van der Pol oscillator system are discussed accordingly.

引用

页码：1377 / 1392

页数：16

共 50 条

[1] DUFFING-VAN DER POL-TYPE OSCILLATOR SYSTEMS [J].

Feng, Zhaosheng .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2014, 7 (06) :1231-1257

[2] FIRST INTEGRALS FOR THE DUFFING-VAN DER POL TYPE OSCILLATOR [J].

Gao, Guangyue ;

Feng, Zhaosheng .

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, :123-133

[3] Hypergeometric first integrals of the Duffing and van der Pol oscillators [J].

Stachowiak, Tomasz .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2019, 266 (09) :5895-5911

[4] A generalization of the S-function method applied to a Duffing-Van der Pol forced oscillator [J].

Braz, A. ;

Duarte, L. G. S. ;

da Mota, L. A. C. P. .

COMPUTER PHYSICS COMMUNICATIONS, 2020, 254

[5] Solutions of an extended Duffing-van der Pol equation with variable coefficients [J].

Cornejo-Perez, O. ;

Albares, P. ;

Negro, J. .

PHYSICA D-NONLINEAR PHENOMENA, 2025, 476

[6] Entrainment of a Van der Pol-Type Circadian Pacemaker to Daylight Cycle [J].

Tayong, F. L. Tsafack ;

Yamapi, R. ;

Filatrella, G. .

BRAZILIAN JOURNAL OF PHYSICS, 2021, 51 (05) :1416-1427

[7] Entrainment of a Van der Pol-Type Circadian Pacemaker to Daylight Cycle [J].

F. L. Tsafack Tayong ;

R. Yamapi ;

G. Filatrella .

Brazilian Journal of Physics, 2021, 51 :1416-1427

[8] An efficient approach to solving fractional Van der Pol-Duffing jerk oscillator [J].

El-Dib, Yusry O. .

COMMUNICATIONS IN THEORETICAL PHYSICS, 2022, 74 (10)

[9] A generalized van der Pol type oscillator: Investigation of the properties of its limit cycle [J].

Kovacic, Ivana ;

Mickens, Ronald E. .

MATHEMATICAL AND COMPUTER MODELLING, 2012, 55 (3-4) :645-653

[10] On the Van der Pol oscillator: An overview [J].

Cveticanin, Livija .

ACOUSTICS & VIBRATION OF MECHANICAL STRUCTURES, 2013, 430 :3-13

← 1 2 3 4 5 →