Title of article :
Toroidal normal forms for bifurcations in retarded functional differential equations I: Multiple Hopf and transcritical/multiple Hopf interaction
Author/Authors :
Younsun Choi، نويسنده , , Victor G. LeBlanc، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2006
Pages :
38
From page :
166
To page :
203
Abstract :
For finite-dimensional bifurcation problems, it is well known that it is possible to compute normal forms which possess nice symmetry properties. Oftentimes, these symmetries may allow for a partial decoupling of the normal form into a so-called “radial” part and an “angular” part. Analysis of the radial part usually gives an enormous amount of valuable information about the bifurcation and its unfoldings. In this paper, we are interested in the case where such bifurcations occur in retarded functional differential equations, and we revisit the realizability and restrictions problem for the class of radial equations by nonlinear delay-differential equations. Our analysis allows us to recover and considerably generalize recent results by Faria and Magalhães [T. Faria, L.T. Magalhães, Restrictions on the possible flows of scalar retarded functional differential equations in neighborhoods of singularities, J. Dynam. Differential Equations 8 (1996) 35–70] and by Buono and Bélair [P.-L. Buono, J. Bélair, Restrictions and unfolding of double Hopf bifurcation in functional differential equations, J. Differential Equations 189 (2003) 234–266].
Keywords :
normal forms , Functional differential equations , realizability , Bifurcations
Journal title :
JOURNAL OF DIFFERENTIAL EQUATIONS
Serial Year :
2006
Journal title :
JOURNAL OF DIFFERENTIAL EQUATIONS
Record number :
750901
Link To Document :
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