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...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.展开更多
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
文摘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.
