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[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]
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Limit cycle problem for quadratic differential system(x·)=-y+lx2+mxy, (y·)=x(1+ax+by)()
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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)
Author(s):
Lu Bingxin;  Luo Dingjun
School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, China
Keywords:
quadratic differential system;  limit cycle;  weak focus
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.

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