两类五次平面多项式系统的中心判定  

Determining Center for Two Quintic Planar Polynomial Systems

作　　者：陈莹[1] 彭真[1] 李静[2] 

机构地区：[1]黄淮学院数学系,河南驻马店463000 [2]北京工业大学应用数理学院,北京100124

出　　处：《河南科技大学学报（自然科学版）》2012年第3期70-74,113-114,共5页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(11072007;10732020);北京市自然科学基金重点项目(1082002);驻马店市自然科学基金项目(09806)

摘　　要：Lyapunov量在平面微分系统的定性理论和分岔理论中占有非常重要的地位,它是判断原点是否为细焦点或中心的一种经典手段,也可以用来判断由退化Hopf分岔所产生的极限环个数,与著名的Hilbert第16问题有密切的关系。主要研究两类五次平面多项式系统的中心判定问题。运用Lyapunov量复算法借助于Maple数学程序计算出两类系统在原点的Lyapunov量,得到原点成为中心的判定条件。Lyapunov values (or equivalent focal values) have very important role in the qualitative theory and bifurcation theory of planar differential systems.It is one classical approach to determine the origin whether is a weak focus or a center and it can also judge the number of limit cycles occurring in degenerate Hopf bifurcation.The computation of Lyapunov values has close relation to the famous Hilbert 16th problem.The problems of determining center for two quintic planar polynomial systems were investigated in this paper.By utilizing the complex algorithm of computing Lyapunov values,the Lyapunov values of two systems were computed under Maple mathematical program.Determinant conditions with origin being a center were also obtained.

关 键 词：五次平面多项式系统 中心 细焦点 Lyapunov量复算法 Maple程序 

分 类 号：O175.12[理学—数学]