Center manifolds and normal forms for a class of retarded functional differential equations with parameter associated with Fold-Hopf singularity

2006 ◽  
Vol 181 (1) ◽  
pp. 220-246 ◽  
Author(s):  
R. Qesmi ◽  
M. Ait Babram ◽  
M.L. Hbid
Keyword(s):  
Differential Equations ◽  
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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