摘要
研究一类平面E13系统的奇点问题,特别是出现细焦点时的Hopf分支问题,以及在某些特定条件下系统在无穷远奇点的性态,进而通过定性分析的方法作出了系统当O(0,0)为中心时的一系列全局相图。
The paper studyies a class of E13 system：x′=yy′=-x＋δy＋a1x2＋a2xy＋b1x3＋b2x2y＋b3xy2when.Using method of bifurcation theory and qualitative analysis,we obtain the global structure of the system in certain condition.It got the following conclusion：（a） When b1〉0,finite critical point O（0,0） can be a fine focus and the highest order of the fine focus O（0,0） is three;so the system has at least three limit cycles.（b）When O（0,0） is a centre,it obtains all the possible global structures of the system through the analysis of the infinite singular points of the system.
出处
《南昌大学学报（理科版）》
CAS
北大核心
2009年第4期315-319,共5页
Journal of Nanchang University(Natural Science)
基金
国家科技支撑资助项目(2008BAI68B01)
