一类pitchfork分支的全局相图  

Global phase portraits of the key pitchfork bifurcation

作　　者：李时敏 Jaume Llibre Shimin Li;Jaume Llibre

机构地区：[1]广东财经大学统计与数学学院,广州510320 [2]Departament de Matemàtiques Universitat Autònoma de Barcelona,Barcelona 08193,Spain

出　　处：《中国科学：数学》2019年第9期1201-1208,共8页Scientia Sinica：Mathematica

基　　金：广州市科技计划(批准号:201707010426和20180401350);广东省自然科学基金(批准号:2017A030313010);the Ministry of Economy and Competitiveness(批准号:MTM 2016-77278-P);Agencia de Gestio d’Ajuts Universitaris i de Recerca(批准号:2017SGR1617);the European project(批准号:Dynamics-H2020-MSCA-RISE-2017-777911);Barcelona Graduate School of Mathematics(批准号:MDM-2014-0445)资助项目

摘　　要：本文研究二次微分系统dt/dr=y^2?y?x,dy/dt=x^2?μx?y,其中μ∈R.该系统是刻画pitchfork分支的重要例子.本文给出该系统在Poincare圆盘上的全局相图。This paper deals with the following quadratic polynomial differential systemdx dt/dr=y^2?y?x,dy/dt=x^2?μx?y,with parameter μ ∈ R, which is the key example for studying the pitchfork bifurcation of a singular point. We classify the global phase portraits in the Poincar′e disc of this system when μ varies.

关 键 词：相图 pitchfork分支 Poincaré紧致化 

分 类 号：C05[社会学] C23