Integrability of Lotka-Volterra Planar Complex Cubic Systems

被引：8
|
作者：
Dukaric, Masa [1 ]
Gine, Jaume [2 ]
机构：
[1] Univ Maribor, Ctr Appl Math & Theoret Phys, Krekova 2, SI-2000 Maribor, Slovenia
[2] Univ Lleida, Dept Matemat, Avda Jaume 2,69, Lleida 25001, Catalonia, Spain
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2016年 / 26卷 / 01期
关键词：
Two-dimensional system; first integral; complex cubic system; integrability; LINEARIZABILITY CONDITIONS; CENTERS;
D O I：
10.1142/S0218127416500024
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the Lotka-Volterra complex cubic systems. We obtain necessary conditions of integrability for these systems with some restriction on the parameters. The sufficiency is proved for all conditions, except one which remains open, using different methods.
引用
收藏
页数：16
相关论文
共 50 条
  • [1] Integrability conditions for Lotka-Volterra planar complex quintic systems
    Gine, Jaume
    Romanovski, Valery G.
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (03) : 2100 - 2105
  • [2] The integrability of a class of cubic Lotka-Volterra systems
    Liu, Changjian
    Li, Yun
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2014, 19 : 67 - 74
  • [3] Linearizability conditions for Lotka-Volterra planar complex cubic systems
    Gine, Jaume
    Romanovski, Valery G.
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2009, 42 (22)
  • [4] Integrability Conditions for Lotka-Volterra Planar Complex Quartic Systems Having Homogeneous Nonlinearities
    Brigita Ferčec
    Jaume Giné
    Yirong Liu
    Valery G. Romanovski
    Acta Applicandae Mathematicae, 2013, 124 : 107 - 122
  • [5] Integrability Conditions for Lotka-Volterra Planar Complex Quartic Systems Having Homogeneous Nonlinearities
    Fercec, Brigita
    Gine, Jaume
    Liu, Yirong
    Romanovski, Valery G.
    ACTA APPLICANDAE MATHEMATICAE, 2013, 124 (01) : 107 - 122
  • [6] Integrability and linearizability of the Lotka-Volterra systems
    Liu, CJ
    Chen, GT
    Li, CZ
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 198 (02) : 301 - 320
  • [7] Local Integrability and Linearizability for Three Dimensional Lotka-Volterra Cubic Systems
    Karim, Aween
    Aziz, Waleed
    Amen, Azad
    QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2025, 24 (01)
  • [8] ON THE INTEGRABILITY OF SOME GENERALIZED LOTKA-VOLTERRA SYSTEMS
    BOUNTIS, TC
    BIER, M
    HIJMANS, J
    PHYSICS LETTERS A, 1983, 97 (1-2) : 11 - 14
  • [9] Integrability of Lotka-Volterra type systems of degree 4
    Liu, Changjian
    Chen, Guoting
    Chen, Guanrong
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 388 (02) : 1107 - 1116
  • [10] Darboux integrability for 3D Lotka-Volterra systems
    Cairó, L
    Llibre, J
    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2000, 33 (12): : 2395 - 2406
12345