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
Source: 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.
Keywords: mixed-mode oscillations; delayed Hopf bifurcation; canards; neuronal modelling; fast-slow dynamics; singular perturbations;Mixed-mode oscillations; Delayed Hopf bifurcation; Canards; Neuronal modelling; Fast-slow dynamics; Singular perturbations
Document URI: http://hdl.handle.net/1942/20672
ISSN: 0096-3003
e-ISSN: 1873-5649
DOI: 10.1016/j.amc.2015.09.083
ISI #: 000365613400031
Rights: © 2015 Elsevier Inc. All rights reserved.
Category: A1
Type: Journal Contribution
Validations: ecoom 2016
Appears in Collections:Research publications

Files in This Item:
File Description SizeFormat 
de maesschalck 1.pdf
  Restricted Access
published version3.08 MBAdobe PDFView/Open    Request a copy
Show full item record

SCOPUSTM   
Citations

7
checked on Sep 3, 2020

WEB OF SCIENCETM
Citations

9
checked on May 21, 2022

Page view(s)

56
checked on May 20, 2022

Download(s)

42
checked on May 20, 2022

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.