BIFURCATION ANALYSIS AND COMPUTATION OF DOUBLE TAKENS-BOGDANOV POINT IN Z_2-EQUIVARIABLE NONLINEAR EQUATIONS  

作　　者：杨忠华 周尉 

机构地区：[1]Department of Mathematics Shanghai Normal University, Shanghai 200234, PRC. [2]Department of Information and Computing Science Zhejiang Institute of Engineering, Hangzhou 310000, PRC.

出　　处：《Numerical Mathematics A Journal of Chinese Universities(English Series)》2005年第4期315-324,共10页

基　　金：Supported by National Natural Science Foundation of China(19971057)Shanghai Development Foundation for Science and Technology(No.00JC14057)Shanghai Science and Technology Committee(No.03QA14036)Doctoral Program of National Higher Education

摘　　要：The paper deals with the computation and bifurcation analysis of double Takens-Bogdanov point (u0, ∧0) (in short, DTB point) in the Z2-equivariable nonlinear equation f(u, ∧) = 0, f: U × R4 → V , where U and V are Banach spaces, parameters ∧∈ R4. At (u0,∧0) , the null spaceof fu0 has geometric multiplicity 2 and algebraic multiplicity 4. Firstly a regular extended system for computing DTB point is proposed. Secondly, it is proved that there are four branches of singular points bifurcated from DTB point: two paths of STB points, two paths of TB-Hopfpoints. Finally,the numerical results of one dimensional Brusselator equations are given to show the effectiveness of our theory and method.The paper deals with the computation and bifurcation analysis of double Takens-Bogdanov point （u^0, A^0） （in short, DTB point） in the Z2-equivariable nonlinear equation f（u,∧） = O, f ： U × R^4 → V , where U and V are Banach spaces, parameters A ∈ R4. At （u^0, ∧^0） , the null space of fo has geometric multiplicity 2 and algebraic multiplicity 4. Firstly a regular extended system for computing DTB point is proposed. Secondly, it is proved that there are four branches of singular points bi.furcated.from DTB point： two paths ofSTB points, two paths o.f TB-Hopf points. Finally, the numerical results of one dimensional Brusselator equations are given to show the effectiveness of our theory and method.

关 键 词：分歧理论 Takens-Bogdanov点 Z2同变 扩展系统 BANACH空间 

分 类 号：O241.82[理学—计算数学]