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http://hdl.handle.net/1942/25866
Title: | Switching to nonhyperbolic cycles from codim-2 bifurcations of equilibria in DDEs | Authors: | BOSSCHAERT, Maikel Janssens, Sebastiaan G. Kuznetsov, Yuri A. |
Issue Date: | 2017 | Source: | 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. | Document URI: | http://hdl.handle.net/1942/25866 | Link to publication/dataset: | https://congressline.hu/enoc2017/abstracts/276.pdf | Category: | C2 | Type: | Conference Material |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
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276.pdf | Conference material | 843.76 kB | Adobe PDF | View/Open |
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