| Limit
Cycle Containing Nine Critical Points in its Interior
for a Class of Cubic Systems |
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| 作者姓名： | LIU Yi rong XIAO Ping |
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| 作者单位： | Department of Applied Mathematics and Applied Software，Central South University of Technology，Changsha 410083，China |
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| 基金项目： | The Natural Science Foundation of Hunan Province !(No .97JJN 70 ) |
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| 摘 要： | Ｉｎｔｈｅｑｕａｌｉｔａｔｉｖｅｔｈｅｏｒｙｏｆｒｅａｌｐｌａｎａｒｄｉｆｆｅｒｅｎｔｉａｌａｕｔｏｎｏｍｏｕｓｓｙｓｔｅｍｓ,ｅｘａｍｐｌｅｓａｎｄｒｅｓｅａｃｈｒｅｓｕｌｔｓａｂｏｕｔｌｉｍｉｔｃｙｃｌｅｓｕｒｒｏｕｎｄｉｎｇａｃｏｍｐｌｅｘｃｒｉｔｉｃａｌｐｏｉｎｔａｒｅｓｅｌｄｏｍｆｏｕｎｄ1,2].Ｕｓｉｎｇｔｈｅｉｎｔｅｒｓｅｃｔｉｏｎｎｕｍｂｅｒｏｆａｌｇｅｂｒａｉｃｃｕｒｖｅ,Ｌｉｕ3]ｄｅｎｏｔｅｓｔｈｅｍｕｌｔｉｐｌｉｃｉｔｙｏｆｃｏｍｐｌｅｘｃｒｉｔｉｃａｌｐｏｉｎｔａｎｄｐｒｏ…
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| 收稿时间： | 28 May 1999 |
Limit cycle containing nine critical points in its interior for a class of cubic systems |
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| LIU Yi rong,XIAO Ping.Limit
Cycle Containing Nine Critical Points in its Interior
for a Class of Cubic Systems[J].Journal of Central South University of Technology,2000,7(2):111-112. |
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| Authors: | Liu Yi-rong and Xiao Ping |
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| Affiliation: | (1) Department of Applied Mathematics and Applied Software, Central South University of Technology, 410083 Changsha, China |
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| Abstract: | Discuss a class of real planar cubic systems with a critical point O (0,0) of nine orders and obtain the conditions for its limit cycle surrounding the origin, and prove that when small pertubations of coefficients are made, the critical point O (0,0) of nine orders is split into nine real simple critical points and the limit cycle surrounding the origin becomes the limit cycle containing nine critical points in its interior. |
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| Keywords: | cubic systems critical point of nine orders limit cycle |
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