LIMIT CYCLES BIFURCATION FOR A CLASS OF DEGENERATE SINGULARITY

被引：0
作者：
Xianping He
Jingjing Feng
Qinlong Wang
机构：
[1] SchoolofInformationandMath,YangtzeUniversity
来源：
AnnalsofDifferentialEquations | 2014年 / 30卷 / 02期
关键词：
limit cycles bifurcation; center manifold; high-order singularity;
D O I：
暂无
中图分类号：
O175 [微分方程、积分方程];
学科分类号：
070104 ;
摘要：
In this paper,bifurcation of limit cycles for the degenerate equilibrium to a threedimensional system is investigated.Firstly,we use formal series to calculate the focal values at the high-order critical point on center manifold.Then an example is studied,and the existence of 3 limit cycles on the center manifold is proved.In terms of highorder singularities in high-dimensional systems,our results are new.
引用
收藏
页码：150 / 156
页数：7
相关论文
共 7 条
[1]  
Limit cycles and singular point quantities for a 3D Lotka–Volterra system[J] . Qinlong Wang,Wentao Huang,Bai-Lian Li. Applied Mathematics and Computation . 2011 (21)
[2]  
A new approach to center conditions for simple analytic monodromic singularities[J] . Isaac A. García,Susanna Maza. Journal of Differential Equations . 2009 (2)
[3]  
Hopf bifurcation for a class of three-dimensional nonlinear dynamic systems[J] . Qinlong Wang,Yirong Liu,Chen Haibo. Bulletin des sciences mathematiques . 2009 (7)
[4]  
A cubic system with twelve small amplitude limit cycles[J] . Yirong Liu,Wentao Huang. Bulletin des sciences mathematiques . 2004 (2)
[5]  
Center conditions and bifurcation of limit cycles at degenerate singular points in a quintic polynomial differential system[J] . Haibo Chen,Yirong Liu,Xianwu Zeng. Bulletin des sciences mathematiques . 2004 (2)
[6]  
A polynomial differential system withnine limit cycles at infinity[J] . Wentao Huang,Yirong Liu. Computers and Mathematics with Applications . 2004 (3)
[7]   Theory of center-focus for a class of higher-degree critical points and infinite points [J].
Liu, YR .
SCIENCE IN CHINA SERIES A-MATHEMATICS, 2001, 44 (03) :365-377
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