Local integrability of a family of three-dimensional quadratic systems

被引：12
作者：
Hu, Zhaoping [1 ,3 ]
Han, Maoan [2 ]
Romanovski, Valery G. [3 ,4 ]
机构：
[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
[2] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China
[3] Univ Maribor, Ctr Appl Math & Theoret Phys, SI-2000 Maribor, Slovenia
[4] Univ Maribor, Fac Nat Sci & Math, SI-2000 Maribor, Slovenia
来源：
PHYSICA D-NONLINEAR PHENOMENA | 2013年 / 265卷
关键词：
Analytic first integrals; Integrability variety; Reversibility; Invariant plane; Darboux integrability; LOTKA-VOLTERRA SYSTEMS; ANALYTIC NORMALIZATION; EMBEDDING FLOWS; LINEARIZABILITY; INTEGRALS;
D O I：
10.1016/j.physd.2013.09.001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We investigate the local integrability of a family of three dimensional quadratic systems in a neighborhood of (0 : -1 : 1) resonant singular point. We find the necessary and sufficient conditions for the existence of two functionally independent first integrals of the system. Mechanisms for integrability for the systems are either time-reversibility or Darboux integrability. (C) 2013 Elsevier B.V. All rights reserved.
引用
收藏
页码：78 / 86
页数：9
相关论文
共 30 条
  • [1] On the global flow of a 3-dimensional Lotka-Volterra system
    Alavez-Ramirez, Justino
    Ble, Gamaliel
    Castellanos, Victor
    Llibre, Jaume
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (10) : 4114 - 4125
  • [2] [Anonymous], 2005, SINGULAR 3 0 COMPUTE
  • [3] [Anonymous], 1999, Qual. Theory Dyn. Syst.
  • [4] [Anonymous], ADV SERIES NONLINEAR
  • [5] [Anonymous], SINGULAR 2 0 LIB COM
  • [6] Local integrability and linearizability of three-dimensional Lotka-Volterra systems
    Aziz, Waleed
    Christopher, Colin
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2012, 219 (08) : 4067 - 4081
  • [7] Inverse Jacobi multipliers
    Lucio R. Berrone
    Hector Giacomini
    [J]. Rendiconti del Circolo Matematico di Palermo, 2003, 52 (1) : 77 - 130
  • [8] BIBIKOV Y. N., 1979, Lecture Notes in Mathematics, V702
  • [9] Mass inflation and chaotic behaviour inside hairy black holes
    Breitenlohner, P
    Lavrelashvili, G
    Maison, D
    [J]. NUCLEAR PHYSICS B, 1998, 524 (1-2) : 427 - 443
  • [10] Bruno A.D., 1989, Local Methods in Nonlinear Differential Equations
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