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

2007 ◽  
Vol 66 (12) ◽  
pp. 2833-2851 ◽  
Author(s):  
R. Qesmi ◽  
M. Ait Babram ◽  
M.L. Hbid
Keyword(s):  
Differential Equations ◽  
Symbolic Computation ◽  
Normal Forms ◽  
Functional Differential Equations ◽  
Center Manifolds ◽  
Retarded Functional Differential Equations ◽  
Functional Differential

Normal forms for periodic retarded functional differential equations

1997 ◽  
Vol 127 (1) ◽  
pp. 21-46 ◽  
Author(s):  
Teresa Faria
Keyword(s):  
Differential Equations ◽  
Normal Forms ◽  
Linear Part ◽  
Functional Differential Equations ◽  
Retarded Functional Differential Equations ◽  
Functional Differential

This paper addresses the computation of normal forms for periodic retarded functional differential equations (FDEs) with autonomous linear part. The analysis is based on the theory previously developed for autonomous retarded FDEs. Adequate nonresonance conditions are derived. As an illustration, the Bogdanov–Takens and the Hopf singularities are considered.

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