| CENTER CONDITIONS AND BIFURCATION OF LIMIT CYCLES FOR A CLASS OF FIFTH DEGREE SYSTEMS |
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| 作者姓名： | HuangWentao LiuYirong |
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| 作者单位： | [1]Dept.ofComput.Sci.andMath.,GuilinUniv.ofElectronicTechnology,Guilin541004,China [2]CollegeofMath.andComput.Tech.,CentralSouthUniv.,Changsha410083,China |
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| 基金项目： | Supported by Science Fund of the Education Departmentof Guangxi province( 2 0 0 3) and the NationalNatural Science Foundation of China( 1 0 361 0 0 3) |
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| 摘 要： | The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated. Two recursive formulas to compute singular quantities at infinity and at the origin are given. The first nine singular point quantities at infinity and first seven singular point quantities at the origin for the system are given in order to get center conditions and study bifurcation of limit cycles. Two fifth degree systems are constructed. One allows the appearance of eight limit cycles in the neighborhood of infinity,which is the first example that a polynomial differential system bifurcates eight limit cycles at infinity. The other perturbs six limit cycles at the origin.
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| 关 键 词： | 极限周值 回归 估计 无穷大 微分学 |
| 收稿时间： | 6 January 2003 |
Center conditions and bifurcation of limit cycles for a class of fifth degree systems |
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| HuangWentao LiuYirong.CENTER CONDITIONS AND BIFURCATION OF LIMIT CYCLES FOR A CLASS OF FIFTH DEGREE SYSTEMS[J].Applied Mathematics A Journal of Chinese Universities,2004,19(2):167-177. |
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| Authors: | Huang Wentao Liu Yirong |
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| Institution: | (1) Dept. of Comput. Sci. and Math., Guilin Univ. of Electronic Technology, 541004 Guilin, China;(2) College of Math. and Comput. Tech., Central South Univ., 410083 Changsha, China |
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| Abstract: | The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated.Two recursive formulas to compute singular quantities at infinity and at the origin are given.The first nine singular point quantities at infinity and first seven singular point quantities at the origin for the system are given in order to get center conditions and study bifurcation of limit cycles.Two fifth degree systems are constructed.One allows the appearance of eight limit cycles in the neighborhood of infinity,which is the first example that a polynomial differential system bifurcates eight limit cycles at infinity.The other perturbs six limit cycles at the origin. |
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| Keywords: | fifth degree system focal value singular point quantity center conditions bifurcation of limit cycles |
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