[1]闫晓芳,尚华辉,杨纪华.具有不变直线的可积非Hamilton系统的极限环分支[J].四川师范大学学报(自然科学版),2018,(03):361-365.[doi:10.3969/j.issn.1001-8395.2018.03.015]
 YAN Xiaofang,SHANG Huahui,YANG Jihua.Bifurcation of Limit Cycles for Integrable Non-Hamilton System with Invariant Straight Lines[J].Journal of SichuanNormal University,2018,(03):361-365.[doi:10.3969/j.issn.1001-8395.2018.03.015]
点击复制

具有不变直线的可积非Hamilton系统的极限环分支()
分享到:

《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03期
页码:
361-365
栏目:
基础理论
出版日期:
2018-03-15

文章信息/Info

Title:
Bifurcation of Limit Cycles for Integrable Non-Hamilton System with Invariant Straight Lines
文章编号:
1001-8395(2018)03-0361-05
作者:
闫晓芳1 尚华辉1 杨纪华2
1.永城职业学院 基础部, 河南 永城 476600;
2.宁夏师范学院 数学与计算机科学学院, 宁夏 固原 756000
Author(s):
YAN Xiaofang1 SHANG Huahui1 YANG Jihua2
1.Department of Basic Education, Yongcheng Vocational College, Yongcheng 476600, Henan;
2.School of Mathematic and Computer Science, Ningxia Normal University, Guyuan 756000, Ningxia
关键词:
可积非Hamilton系统 不变直线 平均法 极限环
Keywords:
integrable non-Hamilton system invariant straight line averaging method limit cycle
分类号:
O175.12
DOI:
10.3969/j.issn.1001-8395.2018.03.015
文献标志码:
A
摘要:
研究如下扰动可积非Hamilton系统(·overx)=-y(ax2+1)+εf(x,y),(·overy)=x(ax2+1)+εg(x,y),其中,a<0,0<|ε|1,f(x,y)和g(x,y)是关于x、y的n次多项式.应用平均法得到该系统至少存在[(n-1)/2]+[(n+1)/2]个极限环.
Abstract:
This paper investigates the following perturbed integrable differential system(·overx)=-y(ax2+1)+εf(x,y),(·overy)=x(ax2+1)+εg(x,y),where a<0,0<|ε|1,f(x,y)and g(x,y)are polynomials in y of degree n. By using the averaging method, we obtain that this system has at least [(n-1)/(2)]+[(n+1)/(2)] limit cycles.

参考文献/References:

[1] ARNOLD V I. Ten problems in:theory of singularities and its applications[J]. Adv Soviet Math,1990,1:1-8.
[2] CHICONE C, JACOBS M. Bifurcation of limit cycles from quadratic isochrones[J]. J Diff Eqns,1991,91(2):268-326.
[3] LI C Z, LLIBRE J, ZHANG Z F. Weak focus, limit cycles and bifurcations for bounded quadratic systems[J]. J Diff Eqns,1995,115(1):193-223.
[4] ATABAIGI A, NYAMORADI N, ZANGENEH H. The number of limit cycles of a quintic polynomial system with a center[J]. Nonlinear Analysis,2009,71(7):3008-3017.
[5] YAO H Y, HAN M A. The number of limit cycles of a class of polynomial differential systems[J]. Nonlinear Analysis,2012,75(1):341-357.
[6] GASULL A, LI C Z, TORREGROSA J. Limit cycles appearing from the perturbation of a system with a multiple line of critical points[J]. Nonlinear Analysis,2012,75(1):278-285.
[7] XIONG Y Q. The number of limit cycles in perturbations of polynomial systems with multiple circles of critical points[J]. J Math Anal Appl,2016,440(1):220-239.
[8] GIACOMINI H, LLIBRE J, VIANO M. On the shape of limit cycles that bifurcate from non-Hamiltonian centers[J]. Nonlinear Analysis,2001,43(7):837-59.
[9] VIANO M, LLIBRE J, GIACOMINI H. Arbitrary order bifurcations for perturbed Hamiltonian planar systems via the reciprocal of an integrating factor[J]. Nonlinear Analysis,2002,48(1):117-36.
[10] LLIBRE J, RIO J, RODRIGUEZ J. Averaging analysis of a perturbated quadratic center[J]. Nonlinear Analysis,2001,46(1):45-51.
[11] GINE J, LLIBRE J. Limit cycles of cubic polynomial vector fields via the averaging theory[J]. Nonlinear Analysis,2007,66(8):1707-1721.
[12] BUICA A, LLIBRE J. Limit cycles of a perturbed cubic polynomial differential center[J]. Chaos, Solitons & Fractals,2007,32(3):1059-1069.
[13] COLL B, LLIBRE J, PROHENS R. Limit cycles bifurcating from a perturbed quartic center[J]. Chaos, Solitons & Fractals,2011,44(4):317-334.
[14] COLL B, GASULL A, PROHENS R. Bifurcation of limit cycles from two families of centers[J]. Dyn Contin Discrete Impuls Syst:Math Anal,2005,12(2):275-287.
[15] VERHULST F. Nonlinear Differential Equations and Dynamical Systems[M]. Berlin:Springer-Verlag,1996.

相似文献/References:

[1]肖辉成.平面射影变换过一不变点至少有一不变直线的一个直接证明[J].四川师范大学学报(自然科学版),1998,(01):0.
 Xiao Huicheng(Yibin Teachers College,Yibin 007,Sichuan).[J].Journal of SichuanNormal University,1998,(03):0.

备注/Memo

备注/Memo:
收稿日期:2016-11-04 接受日期:2017-06-28
基金项目:国家自然科学基金(11701306)和河南省高等学校重点科研项目(17B110003)
第一作者简介:闫晓芳(1980—),女,讲师,主要从事微分方程及其应用的研究,E-mail:jihuall13@163.com
更新日期/Last Update: 2018-03-15