Darboux integrability and algebraic invariant surfaces for the Rikitake system

被引：10

作者：

Llibre, Jaume ^{[1
]}

Valls, Claudia ^{[2
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, Spain

[2] Inst Super Tecn, Dept Matemat, P-1049001 Lisbon, Portugal

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2008年 / 49卷 / 03期

关键词：

D O I：

10.1063/1.2897983

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper, we study the Darboux integrability of the Rikitake system (x)over dot = -mu x + yz, (y)over dot = - mu y+x(z-a), (z)over dot = 1-xy. More precisely, we characterize all the invariant algebraic surfaces, the exponential factors, and the polynomial, rational, and Darboux first integrals of this system according to the values of its parameters a and mu. (C) 2008 American Institute of Physics.

引用

页数：17

共 50 条

[41] Darboux Integrability For Polynomial Vector Fields Invariant Under Action of Finite Group
Correa, Mauricio, Jr.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2012, 11 (01) : 159 - 166
[42] Darboux Integrability For Polynomial Vector Fields Invariant Under Action of Finite Group
Maurício Corrêa
Qualitative Theory of Dynamical Systems, 2012, 11 : 159 - 166
[43] DARBOUX INTEGRABILITY AND RATIONAL REVERSIBILITY IN CUBIC SYSTEMS WITH TWO INVARIANT STRAIGHT LINES
Cozma, Dumitru
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2013,
[44] On the non-integrability of a generalized Darboux Halphen system
Valls, Claudia
JOURNAL OF GEOMETRY AND PHYSICS, 2006, 57 (01) : 89 - 100
[45] Darboux integrability of generalized Yang—Mills Hamiltonian system
Jaume Llibre
Claudia Valls
Journal of Nonlinear Mathematical Physics, 2016, 23 : 234 - 242
[46] Invariant algebraic surfaces for a virus dynamics
Valls, Claudia
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2015, 66 (04): : 1315 - 1328
[47] Invariant algebraic surfaces for a virus dynamics
Claudia Valls
Zeitschrift für angewandte Mathematik und Physik, 2015, 66 : 1315 - 1328
[48] Global dynamics of the Maxwell-Bloch system with invariant algebraic surfaces
Dias, F. S.
Valls, Claudia
DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2020, 35 (04): : 668 - 681
[49] Dynamics of the FitzHugh-Nagumo system having invariant algebraic surfaces
Llibre, Jaume
Tian, Yuzhou
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2021, 72 (01):
[50] Comment on 'The Darboux transformation and algebraic deformations of shape-invariant potentials
Sinha, A
Roy, P
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2004, 37 (34): : 8401 - 8404

← 1 2 3 4 5 →