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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/20672

Title: Sector-delayed-Hopf-type mixed-mode oscillations in a prototypical three-time-scale model
Authors: De Maesschalck, Peter
Kutafina, Ekaterina
Popovic, N.
Issue Date: 2016
Publisher: ELSEVIER SCIENCE INC
Citation: APPLIED MATHEMATICS AND COMPUTATION, 273, p. 337-352
Abstract: We consider a three-dimensional three-time-scale system that was first proposed by Krupa et al. (2008) under the additional assumption that two singular perturbation parameters are present in the equations. While the presence of three scales was shown to give use to canard induced periodic mixed mode oscillations (MMOs) (Desroches et al., 2012) in the parameter regime studied by Krupa et al. (2008,) we additionally observe mixed mode patterns that display delayed-Hopf-type behaviour (Neishtadt, 1987). We present analytical and numerical evidence for the occurrence of stable periodic dynamics that realises both mechanisms, and we discuss the transition between them. To the best of our knowledge, the resulting mixed sector-delayed-Hopf-type MMO trajectories represent a novel class of mixed-mode dynamics in singularly perturbed systems of ordinary differential equations. (C) 2015 Elsevier Inc. All rights reserved.
Notes: [De Maesschalck, P.] Hasselt Univ, B-3590 Diepenbeek, Belgium. [Kutafina, E.] AGH Univ Sci & Technol, PL-30059 Krakow, Poland. [Kutafina, E.] Uniklin RWTH Aachen, Dept Med Informat, D-52057 Aachen, Germany. [Popovic, N.] Univ Edinburgh, Sch Math, Edinburgh EH9 3FD, Midlothian, Scotland. [Popovic, N.] Univ Edinburgh, Maxwell Inst Math Sci, Edinburgh EH9 3FD, Midlothian, Scotland.
URI: http://hdl.handle.net/1942/20672
DOI: 10.1016/j.amc.2015.09.083
ISI #: 000365613400031
ISSN: 0096-3003
Category: A1
Type: Journal Contribution
Validation: ecoom, 2016
Appears in Collections: Research publications

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