4类平面多项式微分系统的Lyapunov量复算法  

Complex Algorithms of Lyapunov Values for Four Plane Polynomial Differential Systems

作　　者：陈莹 杨金根 何斌[3] 李静[3] CHEN Ying;YANG Jingen;HE Bin;LI Jing(School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China;School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China;College of Applied Sciences, Beijing University of Technology, Beijing 100124, China)

机构地区：[1]黄淮学院数学与统计学院,河南驻马店463000 [2]信阳师范学院数学与统计学院,河南信阳464000 [3]北京工业大学应用数理学院,北京100124

出　　处：《济南大学学报（自然科学版）》2018年第2期156-160,共5页Journal of University of Jinan(Science and Technology)

基　　金：国家自然科学基金项目(11372014);北京市自然科学基金项目(1172002)

摘　　要：为了研究平面多项式微分系统的Lyapunov量复算法和原点的类型,通过Lyapunov量复算法计算得出4类微分系统的Lyapunov量;得到前2类系统的原点成为中心的充分条件和原点成为最高阶细焦点的阶数,同时判断在不同参数数据时最高阶细焦点的稳定性;讨论加单扰动项和双扰动项的后2类系统的Lyapunov量的复计算。结果表明:原点成为前2类系统的最高阶细焦点的阶数分别为4和3;在不同的控制参数组时后2类系统的原点类型为中心、一阶稳定细焦点和一阶不稳定细焦点。To investigate complex algorithms of Lyapunov values and types of origin for plane polynomial differential systems,Lyapunov values for four differential systems were computed with complex algorithms of Lyapunov values.Sufficient conditions with origin being a center and the highest orders of fine focus were obtained for the first two systems,and the stabilities of the highest-order fine focus were judged under different parameter data.Complex computations of Lyapunov values for the last two systems with only one perturbation term and two perturbation terms were respectively discussed.The results show that the orders of origin being the highest order of fine focus for the first two systems respectively are four and three.Types of origin for the last two systems with different control parameter groups are center,the first-order stable fine focus,and the first-order unstable fine focus.

关 键 词：Lyapunov量 多项式微分系统 中心 细焦点 稳定性 

分 类 号：O175.12[理学—数学]