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
收藏
页数：17
相关论文
共 50 条
  • [1] Invariant algebraic surfaces of the Rikitake system
    Llibre, J
    Zhang, X
    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2000, 33 (42): : 7613 - 7635
  • [2] Darboux integrability and invariant algebraic curves for planar polynomial systems
    Christopher, C
    Llibre, J
    Pantazi, C
    Zhang, X
    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2002, 35 (10): : 2457 - 2476
  • [3] Darboux polynomials and algebraic integrability of the Chen system
    Lu, Tinghua
    Zhang, Xiang
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2007, 17 (08): : 2739 - 2748
  • [4] Analytical integrability of the Rikitake system
    Llibre, Jaume
    Valls, Claudia
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2010, 61 (04): : 627 - 634
  • [5] Analytical integrability of the Rikitake system
    Jaume Llibre
    Clàudia Valls
    Zeitschrift für angewandte Mathematik und Physik, 2010, 61 : 627 - 634
  • [6] DARBOUX POLYNOMIALS AND NON-ALGEBRAIC INTEGRABILITY OF THE L SYSTEM
    Tinghua L (Dept. of Math.
    Annals of Applied Mathematics, 2009, (04) : 420 - 431
  • [7] DARBOUX POLYNOMIALS AND NON-ALGEBRAIC INTEGRABILITY OF THE L SYSTEM
    Tinghua L Dept of Math Shandong Institute of Business and Technology Yantai Shandong
    Annals of Differential Equations, 2009, 25 (04) : 420 - 431
  • [8] Invariant surfaces and Darboux integrability for non-autonomous dynamical systems in the plane
    Demina, Maria, V
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2018, 51 (50)
  • [9] Invariant algebraic surfaces of the Lorenz system
    Llibre, J
    Zhang, X
    JOURNAL OF MATHEMATICAL PHYSICS, 2002, 43 (03) : 1622 - 1645
  • [10] INVARIANT ALGEBRAIC SURFACES OF THE CHEN SYSTEM
    Deng, Xijun
    Chen, Aiyong
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2011, 21 (06): : 1645 - 1651
12345