一类广义Riccati系统极限环和局部临界周期分支  

Limit Cycles and Local Critical Periods for a Class of Generalized Riccati System

作　　者：刘园园 黄文韬[2] LIU Yuan-yuan;HUANG Wen-tao(School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin Guangxi 541004, China;Guilin University of Aerospace Technology, Guilin Guangxi 541004, China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004 [2]桂林航天工业学院,广西桂林541004

出　　处：《西南师范大学学报（自然科学版）》2020年第9期6-12,共7页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11461021);广西自然科学基金重点项目(2016GXNSFDA380031).

摘　　要：研究了一类广义Riccati系统在原点处的极限环与局部临界周期分支问题.通过计算其伴随复系统的奇点量,导出系统原点为中心的必要条件,运用对称原理证明了系统原点成为中心的充分条件,进一步得到系统原点成为6阶细焦点的条件.由周期常数的计算得到了系统原点为3阶细中心的条件.分别证明了系统在原点处可分支出6个极限环与3个局部临界周期分支,得到了三次Riccati系统极限环数和局部临界周期数的最好结果.The limit cycle and local critical period bifurcation of a class of generalized Riccati systems at the origin have been investigated.By computing the singular point values of the origin of the system,the necessary conditions for the origin to be the center have been deduced.The sufficient conditions have been proved by the symmetry principle.Moreover,the conditions of the origin to be the six order fine focus have been given.By computing the period constants of the origin of the system,the conditions of the origin to be the three order fine center have been obtained.It is proved respectively that there are six small amplitude limit cycles bifurcated at the origin and three local critical periods bifurcated at the origin.As far as we known,there are the best results of the number of limit cycles and local critical periods for the cubic generalized Riccati systems.

关 键 词：广义RICCATI方程 奇点量 中心 极限环 局部临界周期分支 

分 类 号：O175.12[理学—数学]