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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/25866

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 [1]. This makes it is possible to apply the normalization method for local bifurcations of ODEs [2] to DDEs. Recently, the critical normal form coefficients for all five codimension 2 bifurcation of equilibria in generic DDEs have been derived [7] and implemented into the Octave/Matlab package DDE-BifTool [5]. We generalize a center manifold theorem from [1] 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.
URI: http://hdl.handle.net/1942/25866
Link to publication: https://congressline.hu/enoc2017/abstracts/276.pdf
Category: C2
Type: Conference Material
Appears in Collections: Research publications

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