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http://hdl.handle.net/1942/31268
Title: | Intrinsic determination of the criticality of a slow-fast Hopf bifurcation | Authors: | DE MAESSCHALCK, Peter Doan, Thai Son WYNEN, Jeroen |
Issue Date: | 2020 | Source: | Abstract: | The presence of slow-fast Hopf (or singular Hopf) points in slow-fast systems in the plane is often deduced from the shape of a vector field brought into normal form. It can however be quite cumbersome to put a system in normal form. In the monograph "Canards from birth to transition", an intrinsic presentation of slow-fast vector fields is initiated, showing hands-on formulas to check for the presence of such singular contact points. We generalize the results in the sense that the criticality of the Hopf bifurcation can be checked with a single formula. We demonstrate the result on a slow-fast system given in non-standard form where slow and fast variables are not separated from each other. The formula is convenient since it does not require any parameterization of the critical curve. | Keywords: | Mathematics - Dynamical Systems;34C23, 37G10, 34C26;singular bifurcations;slow-fast Hopf bifurcation;criticality | Document URI: | http://hdl.handle.net/1942/31268 | Link to publication/dataset: | http://arxiv.org/abs/2005.10742v1 | Category: | O | Type: | Preprint |
Appears in Collections: | Research publications |
Files in This Item:
File | Description | Size | Format | |
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2005.10742v1.pdf | Non Peer-reviewed author version | 196.49 kB | Adobe PDF | View/Open |
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