| 一类四次系统的幂零中心条件与极限环分支 |
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| 引用本文： | 鹿永梅,刘一戎.一类四次系统的幂零中心条件与极限环分支[J].邵阳学院学报(自然科学版),2011,8(1):14-19. |
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| 作者姓名： | 鹿永梅 刘一戎 |
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| 作者单位： | 浙江师范大学数理信息工程学院,浙江金华,321004 |
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| 基金项目： | 国家自然科学基金项目(11071222) |
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| 摘 要： | 本文研究了一类原点为三次幂零奇点的四次系统的中心焦点判定和极限环分支问题,给出了一类四次系统计算原点拟Lyapunov常数的递推公式,并得到了该系统原点的前9个拟Lyapunov常数b及原点成为中心和最高阶细焦点的充分必要条件,由此得到了该系统的扰动系统在原点充分小的邻域内恰有9个包围原点的极限环的结论.
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| 关 键 词： | 四次系统 幂零奇点 拟Lyapunov常数 中心焦点问题 极限环分支 |
Conditions of Nilpotent Center and Limit Cycle Bifurcation for a Class of Special Quartic System |
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| LU Yong-mei,LIU Yirong.Conditions of Nilpotent Center and Limit Cycle Bifurcation for a Class of Special Quartic System[J].Journal of Shaoyang University:Science and Technology,2011,8(1):14-19. |
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| Authors: | LU Yong-mei LIU Yirong |
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| Institution: | LU Yong-mei,LIU Yirong(Department of Mathematics,Zhejiang Normal University,Jinhua,Zhejiang,321004,China) |
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| Abstract: | A class of quartic differential system in which origin nilpotent singular point is studied in this paper.By a recursive formula,the first nine quasi-Lyapunov constants of the system are derived,from which the conditions for origin is a center and the highest degree fine focus are given.Correspondingly,by small perturbation,we prove that there exist nine small amplitude limit cycles in the neighborhood of the nilpotent singular point. |
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| Keywords: | quartic system nilpotent singular point quasi-Lyapunov constants center-focus problem bifurcation of limit cycles |
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