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|Title: ||Switching to nonhyperbolic cycles from codim-2 bifurcations of equilibria in DDEs|
|Authors: ||Bosschaert, Maikel M.|
Janssens, Sebastiaan G.
Kuznetsov, Yuri A.
|Issue Date: ||2017|
|Citation: ||9th European Nonlinear Dynamics Conference (ENOC 2017), Budapest University of Technology and Economics, Budapest, Hungary, 25-30/06/2017|
|Abstract: ||Using the framework of dual semigroups, the existence of a finite dimensional smooth center manifold for DDEs can be
rigorously established . This makes it is possible to apply the normalization method for local bifurcations of ODEs  to DDEs.
Recently, the critical normal form coefficients for all five codimension 2 bifurcation of equilibria in generic DDEs have been derived
 and implemented into the Octave/Matlab package DDE-BifTool . We generalize a center manifold theorem from 
to generic parameter-dependent DDEs, covering the cases where the critical equilibrium can disappear. It allows us to initialize the
continuation of codimension 1 equilibrium and nonhyperbolic cycle bifurcations emanating from the generalized Hopf, zero-Hopf and
Hopf-Hopf bifurcations in DDEs, which are the only codim 2 eqillibrium bifurcations in generic DDEs where nonhyperbolic cycles
could originate. The obtained expressions have been implemented in DDE-BifTool and tested on various models.|
|Link to publication: ||https://congressline.hu/enoc2017/abstracts/276.pdf|
|Type: ||Conference Material|
|Appears in Collections: ||Research publications|
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