Symbolic computation for center manifolds and normal forms of Bogdanov bifurcation in retarded functional differential equations

[1]  R. I. Bogdanov Versal deformations of a singular point of a vector field on the plane in the case of zero eigenvalues , 1975 .

[2]  L. Chua,et al.  Normal forms for nonlinear vector fields. I. Theory and algorithm , 1988 .

[3]  S. Wiggins Introduction to Applied Nonlinear Dynamical Systems and Chaos , 1989 .

[4]  André Vanderbauwhede,et al.  Center Manifold Theory in Infinite Dimensions , 1992 .

[5]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[6]  Jack K. Hale,et al.  Period Doubling in Singularly Perturbed Delay Equations , 1994 .

[7]  S. Chow,et al.  Normal Forms and Bifurcation of Planar Vector Fields , 1994 .

[8]  L. Magalhães,et al.  Normal Forms for Retarded Functional Differential Equations and Applications to Bogdanov-Takens Singularity , 1995 .

[9]  S. Lunel,et al.  Delay Equations. Functional-, Complex-, and Nonlinear Analysis , 1995 .

[10]  L. Magalhães,et al.  Normal Forms for Retarded Functional Differential Equations with Parameters and Applications to Hopf Bifurcation , 1995 .

[11]  O. Arino,et al.  Approximation Scheme of a Center Manifold for Functional Differential Equations , 1997 .

[12]  O. Arino,et al.  Computational Scheme of a Center Manifold for Neutral Functional Differential Equations , 2001 .

[13]  Redouane Qesmi,et al.  A Maple program for computing a terms of a center manifold, and element of bifurcations for a class of retarded functional differential equations with Hopf singularity , 2006, Appl. Math. Comput..