Integrability of Van der Pol-Duffing oscillator system in three-dimensional vector field

被引：4

作者：

Hussein, Niazy Hady ^{[1
]}

Amen, Azad Ibrahim ^{[2
,3
]}

机构：

[1] Soran Univ Erbil, Dept Math, Fac Sci, Erbil, Iraq

[2] Salahaddin Univ Erbil, Dept Math, Basic Educ Coll, Erbil, Iraq

[3] Raparin Univ Ranya, Dept Math, Basic Educ Coll, Ranya, Iraq

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2022年 / 45卷 / 03期

关键词：

analytic first integrals; Darboux first integrals; exponential factors; invariant algebraic surfaces; 3D Van der Pol-Duffing system; INVARIANT ALGEBRAIC-CURVES; SYNCHRONIZATION;

D O I：

10.1002/mma.7876

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, we focus on studying the integrability of the following three-dimensional Van der Pol-Duffing system (x) over dot =-m(x(3) - mu x - y), (y) over dot = x - y - z, (z) over dot = beta y. More precisely, if m beta not equal 0, then the above system has no analytic and nor Darboux first integrals at the neighborhood of the origin. Also, the stability and instability of the singular points are employed to investigate the C-1 integrability of this type of system.

引用

页码：1597 / 1611

页数：15

共 19 条

[1]

Christopher C., 1999, QUAL THEORY DYN SYST, V1, P71

[2]

Christopher C., 2000, ANN DIFFERENTIAL EQU, V16, P5

[3] INVARIANT ALGEBRAIC-CURVES AND CONDITIONS FOR A CENTER [J].

CHRISTOPHER, CJ .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1994, 124 :1209-1229

[4] Multiplicity of invariant algebraic curves in polynomial vector fields [J].

Christopher, Colin ;

Llibre, Jaume ;

Pereira, Jorge Vitorio .

PACIFIC JOURNAL OF MATHEMATICS, 2007, 229 (01) :63-117

[5] Adaptive synchronization of two chaotic systems consisting of modified Van der Pol-Duffing and Chua oscillators [J].

Fotsin, H ;

Bowong, S ;

Daafouz, J .

CHAOS SOLITONS & FRACTALS, 2005, 26 (01) :215-229

[6]

Gantmacher FR., 2005, APPL THEORY MATRICES, V1

[7]

Jordan DW., 1999, NONLINEAR ORDINARY D

[8] Integrability of the Rucklidge system [J].

Lima, Mauricio F. S. ;

Llibre, Jaume ;

Valls, Claudia .

NONLINEAR DYNAMICS, 2014, 77 (04) :1441-1453

[9]

Llibre J., 2012, INT J BIFURCAT CHAOS, V22

[10]

Llibre J, 2008, ADV NONLINEAR STUD, V8, P871

← 1 2 →