DISTRIBUTIONS OF LIMIT CYCLES FOR POLYNOMIAL VECTOR FIELDS (P_2, Q_3)  

作　　者：肖敏 罗定军 

机构地区：[1]Dept. of Math., Nanjing Xiao Zhuan Narmal College, Nanjing 210017 [2]School of Math, and Computer Sciences, Nanjing Normal University, Nanjing 210097

出　　处：《Annals of Differential Equations》2003年第1期84-92,共9页微分方程年刊（英文版）

基　　金：Supported by National Natural Science Foundations of China (No. 19871041).

摘　　要：The distributions of limit cycles of cubic vector fields (P2, Q3) are considered in this paper, where P2 and Q3 are polynomials of x and y of order two and three, respectively. It is possibly seven different distributions of limit cycles given in [1]. We now prove that in which three kinds of distributions are impossible and other four kinds all can be realized by concrete vector fields of (P2,Q3). Some related results are also given.The distributions of limit cycles of cubic vector fields (P2, Q3) are considered in this paper, where P2 and Q3 are polynomials of x and y of order two and three, respectively. It is possibly seven different distributions of limit cycles given in [1]. We now prove that in which three kinds of distributions are impossible and other four kinds all can be realized by concrete vector fields of (P2,Q3). Some related results are also given.

关 键 词：distribution of limit cycles BIFURCATION 

分 类 号：O174.14[理学—数学]