LINEAR RECURSION FORMULAS OF GENERALIZED FOCUS QUANTITIES AND LOCAL INTEGRABILITY FOR A CLASS OF THREE-DIMENSIONAL SYSTEMS

被引：0

作者：

Wang, Qinlong ^{[1
]}

Li, Wenyu ^{[1
]}

Huang, Wentao ^{[2
]}

机构：

[1] Guilin Univ Elect Technol, Sch Math & Computat Sci, Guilin 541004, Guangxi, Peoples R China

[2] Guangxi Normal Univ, Coll Math & Stat, Ctr Appl Math Guangxi, Guilin 541006, Peoples R China

来源：

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2022年 / 12卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Three-dimensional system; integrability; power series method; generalized focus quantity; RESONANT CENTER PROBLEM; LINEARIZABILITY; CENTERS; POINTS;

D O I：

10.11948/20220178

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the local integrability of a class of three-dimensional systems is studied. The recursive formulas to compute the generalized focus quantities of the system are deduced firstly, then they are applied to a Lotka-Volterra system. The integrable conditions of the system are obtained and the local integrability is solved completely. The algorithm corresponding to the above formulas is an extension and development of the power series method for the planar differential systems with p : -q arbitrary resonant saddle point and also readily done with using computer algebra system such as Mathematica or Maple.

引用

页码：1186 / 1194

页数：9

共 26 条

[11]

Dulac H., 1908, Bull. Sci. Math. Ser., V32, P230

[12]

Fronville A, 1998, FUND MATH, V157, P191

[13] Integrability conditions for Lotka-Volterra planar complex quintic systems [J].

Gine, Jaume ;

Romanovski, Valery G. .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (03) :2100-2105

[14] Integrability and linearizability of the Lotka-Volterra system with a saddle point with rational hyperbolicity ratio [J].

Gravel, S ;

Thibault, P .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2002, 184 (01) :20-47

[15] 1:-3 resonant centers on C2 with homogeneous cubic nonlinearities [J].

Hu, Zhaoping ;

Romanovski, Valery G. ;

Shafer, Douglas S. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (08) :1927-1940

[16] Complex integrability and linearizability of cubic Z2-equivariant systems with two 1:q resonant singular points [J].

Li, Feng ;

Liu, Yuanyuan ;

Yu, Pei ;

Wang, Jinliang .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 300 :786-813

[17] Complex isochronous centers and linearization transformations for cubic Z2-equivariant planar systems [J].

Li, Feng ;

Liu, Yirong ;

Liu, Yuanyuan ;

Yu, Pei .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 268 (07) :3819-3847

[18] Integrability and linearizability of the Lotka-Volterra systems [J].

Liu, CJ ;

Chen, GT ;

Li, CZ .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 198 (02) :301-320

[19]

Romanovski V.G., 2009, The Center and Cyclicity Problems: a Computational Algebra Approach

[20] On the Center Problem for p : -q Resonant Polynomial Vector Fields [J].

Romanovski, Valery G. ;

Shafer, Douglas S. .

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2008, 15 (05) :871-887

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