[1]唐 璐,陆征一*,杨 静.一类三次微分系统中心存在的条件[J].四川师范大学学报(自然科学版),2018,(05):586-590.[doi:10.3969/j.issn.1001-8395.2018.05.003]
 TANG Lu,LU Zhengyi,YANG Jing.The Center Conditions for a Class of Cubic Differential Systems[J].Journal of SichuanNormal University,2018,(05):586-590.[doi:10.3969/j.issn.1001-8395.2018.05.003]
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一类三次微分系统中心存在的条件()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2018年05期
页码:
586-590
栏目:
基础理论
出版日期:
2018-06-15

文章信息/Info

Title:
The Center Conditions for a Class of Cubic Differential Systems
文章编号:
1001-8395(2018)05-0586-05
作者:
唐 璐1 陆征一2* 杨 静12
1.四川师范大学 数学与软件科学学院, 四川 成都 610066; 2.中国科学院 成都计算机应用研究所, 四川 成都 610041
Author(s):
TANG Lu1 LU Zhengyi2 YANG Jing12
1.College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, Sichuan; 2.Institute of Computer Applications, Academia Sinica, Chengdu 610041, Sichuan
关键词:
三次系统 中心问题 代数对称 中心条件
Keywords:
cubic systems center problem algebraic symmetric center condition
分类号:
O175
DOI:
10.3969/j.issn.1001-8395.2018.05.003
文献标志码:
A
摘要:
考虑一类三次微分系统中心问题,通过代数对称法得到系统中心的三组新的充分条件.
Abstract:
In this paper, the center problem of a class of cubic differential systems is considered.Three new sets of sufficient conditions are obtained through the algebraic symmetries method.

参考文献/References:

[1] LI J. Hilbert's 16th problem and bifurcations of planar polynomial vector fields[J]. Inter J Bifurcation Chaos,2003,13(1):47-106.
[2] WAND D M. Mechanical manipulation for a class of differential system[J]. J Symb Comp,1991,12(2):233-254.
[3] GINE J, SANTALLUSIA X. On the Poincare-Liapunov constants and Poincare series[J]. Appl Math Warsaw,2001,28(1):17-30.
[4] LU Z Y, LUO Y. Two limit cycles in three dimensional Lotka-Volterra systems[J]. Comp Math Appl,2002,44(2):51-66.
[5] DULAC H. Dtermination et intgration d'une certaine classe dquations diffrentielles ayant pour point singulier un centre[J]. Bull Sci Math,1908,32(1):230-252.
[6] KAPTEYN W. Over de middlepunten der integral krommen van differential vergelijkingen van de eerste orde en den eerstengraad[J]. Kon Ned Akad Wet Versl,1911,14(19):1446-1457.
[7] BAUTIN N N. On the numer of limit cycles which appear with the variation of the coefficients from an equilibrium position of focus or a center type[J]. Mat Sbornik NS,1952,30(72):181-196.
[8] WANG D M. A class of cubic differential systems with 6-tuple focus[J]. J Diff Eqns,1990,87(2):305-315.
[9] 桑波. 常微分方程定性理论中的中心焦点及相关问题[D]. 广州:中山大学,2006.
[10] XU J, LU Z Y. Sufficient and necessary center conditions for the poincare systems P(2,2n)(n≤5)[J]. J Appl Math,2011,2011(2):1-18.
[11] CHRISTOPHER C J, LYNCH S. Small-amplitude limit cycle bifurcations for lienard systems with quadratic or cubic damping or restoringforces[J]. Nonlinearilty,1999,12(12):1099-1112.
[12] CHRISTOPHER C J, SCHLOMIUK D. Center conditions for a class of polynomial differential system[J]. Discrete Contin Dyn Syst,2015,35(3):1075-1090.
[13] CHRISTOPHER C J. SCHLOMIUK D. On general algebraic mechanisms for producing centers in polynomial differential systems[J]. J Fixed Point Theory Applications,2008,3(2):331-351.
[14] DARBOUX G. Mmoire sur les quations differentielles algbriques du premier ordre et du premier degr[J]. Bull Sci Math,1878,2(32):60-96.
[15] LLIBRE J, RAMIREZ R, SADOVSKAIA N. On the 16th Hilbert problem for algebraic limit cycles[J]. J Diff Eqns,2010,248(6):1401-1409.
[16] PEARSON J M, LLOYD N G, CHRISTOPHER C J. Algorithmic Derivation of Center Conditions[J]. Society for Industrial and Applied Mathematics,1996,38(4):619-636.
[17] 杨静,陆征一. Lotka-Volterra 系统与Kolmogorov 系统极限环的存在性与中心焦点的算法化判定[J]. 应用数学,2016,29(4):731-737.
[18] 胡亦郑. 几类平面多项式微分系统中心型奇点算法化判定[D]. 成都:中国科学院成都计算机研究所,2012.
[19] 陆征一,何碧,罗勇. 多项式系统的实根分离算法及其应用[M]. 北京:科学出版社,2004.
[20] 徐金亚. 一类Poincare 系统的中心条件及小扰动极限环最大个数估计的算法化推导[D]. 成都:中国科学院成都计算机研究所,2011.

备注/Memo

备注/Memo:
收稿日期:2016-11-22 接受日期:2017-04-06
资金项目:教育部博士点基金(20115134110001)
*通信作者简介:陆征一(1962—),男,教授,主要从事常微分方程定性理论的研究,E-mail:zhengyilu@hotmail.com
更新日期/Last Update: 2018-04-15