|Table of Contents|

[1] Lu Bingxin, Luo Dingjun,. Limit cycle problem for quadratic differential system(x·)=-y+lx2+mxy, (y·)=x(1+ax+by) [J]. Journal of Southeast University (English Edition), 2004, 20 (4): 517-520. [doi:10.3969/j.issn.1003-7985.2004.04.025]
Copy

Limit cycle problem for quadratic differential system(x·)=-y+lx2+mxy, (y·)=x(1+ax+by)()
二次微分系统(x·)=-y+lx2+mxy, (y·)=x(1+ax+by)的极限环问题
Share：

Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
20
Issue:
2004 4
Page:
517-520
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2004-12-30

Info

Title:
Limit cycle problem for quadratic differential system(x·)=-y+lx2+mxy, (y·)=x(1+ax+by)
二次微分系统(x·)=-y+lx2+mxy, (y·)=x(1+ax+by)的极限环问题
Author(s):
Lu Bingxin, Luo Dingjun
School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, China
陆炳新, 罗定军
南京师范大学数学与计算机科学学院, 南京 210097
Keywords:
quadratic differential system;  limit cycle;  weak focus
二次微分系统;  极限环;  细焦点
PACS:
O175.12
DOI:
10.3969/j.issn.1003-7985.2004.04.025
Abstract:
The maximal number of limit cycles for a particular type Ⅲ system (x·)=-y+lx2+mxy, (y·)=x(1+ax+by) is studied and some errors that appeared in the paper by Suo Mingxia and Yue Xiting (Annals of Differential Equations, 2003, 19(3):397-401)are corrected. By translating the system to be considered into the Liénard type and by using some related properties, we obtain several theorems with suitable conditions coefficients of the system, under which we prove that the system has at most two limit cycles. The conclusions improve the results given in Suo and Yue’s paper mentioned above.
研究了特殊Ⅲ类二次微分系统(x·)=-y+lx2+mxy, (y·)=x(1+ax+by)的极限环的最大个数问题. 纠正了索明霞和岳锡亭的文章(微分方程年刊, 2003, 19(3):397-401)中的一些错误. 通过将所研究的系统化为Liénard型系统并利用其相关性质给出了几个定理, 在某些条件下证明了系统最多存在2个极限环, 改进了上述一文中的结果.

References:

[1] Ye Yanqian. Theory of limit cycles[M]. Shanghai: Shanghai Scientific and Technical Publishers, 1984.(in Chinese)
[2] Ye Yanqian. Qualitative theory of polynomial differential systems[M]. Shanghai: Shanghai Scientific and Technical Publishers, 1995.(in Chinese)
[3] Cai Suilin. Case of research of quadratic system[J]. Advances in mathematics, 1989, 18: 5-12.
[4] Suo Mingxia, Yue Xiting. The maximal number of limit cycles for quadratic differential system (·overx)=-y+lx2+xy, (·overy)=x(21+ax+by)[J]. Annals of Differential Equations, 2003, 19(3): 397-401.
[5] Xie Xiangdong. On the nonexistence of LCs of type(Ⅲ)n=0[J]. Annals of Differential Equations, 1992, 8(1): 98-103.

Memo

Memo:
Biographies: Lu Bingxin(1963—), male, associate professor, LuBingxin@njnu.edu.cn; Luo Dingjun(corresponding author), male, professor, djluo@njnu.edu.cn.
Last Update: 2004-12-20