dc.contributor.author | Uria Albizuri, Jone | |
dc.contributor.author | Desroches, Mathieu | |
dc.contributor.author | Krupa, Martin | |
dc.contributor.author | Rodrigues, Serafim | |
dc.date.accessioned | 2024-02-08T10:18:48Z | |
dc.date.available | 2024-02-08T10:18:48Z | |
dc.date.issued | 2020-09-07 | |
dc.identifier.citation | Journal of Nonlinear Science 30 : 3265-3291 (2020) | |
dc.identifier.issn | 0938-8974 | |
dc.identifier.uri | http://hdl.handle.net/10810/65244 | |
dc.description.abstract | Specific kinds of physical and biological systems exhibit complex Mixed-Mode Oscillations mediated by folded-singularity canards in the context of slow-fast models. The present manuscript revisits these systems, specifically by analysing the dynamics near a folded singularity from the viewpoint of inflection sets of the flow. Originally, the inflection set method was developed for planar systems [Brøns and Bar-Eli in Proc R Soc A 445(1924):305–322, 1994; Okuda in Prog Theor Phys 68(6):1827–1840, 1982; Peng et al. in Philos Trans R Soc A 337(1646):275–289, 1991] and then extended to N-dimensional systems [Ginoux et al. in Int J Bifurc Chaos 18(11):3409–3430, 2008], although not tailored to specific dynamics (e.g. folded singularities). In our previous study, we identified components of the inflection sets that classify several canard-type behaviours in 2D systems [Desroches et al. in J Math Biol 67(4):989– 1017, 2013]. Herein, we first survey the planar approach and show how to adapt it for 3D systems with an isolated folded singularity by considering a suitable reduction of such 3D systems to planar non-autonomous slow-fast systems. This leads us to the computation of parametrized families of inflection sets of one component of that planar (non-autonomous) system, in the vicinity of a folded node or of a folded saddle. We then show that a novel component of the inflection set emerges, which approximates and follows the axis of rotation of canards associated to folded-node and folded-saddle singularities. Finally, we show that a similar inflection-set component occurs in the vicinity of a delayed Hopf bifurcation, a scenario that can arise at the transition between folded node and folded saddle. These results are obtained in the context of a canonical model for folded-singularity canards and subsequently we show it is also applicable to complex slow-fast models. Specifically, we focus the application towards the self-coupled 3D FitzHugh–Nagumo model, but the method is generically applicable to higher-dimensional models with isolated folded singularities, for instance in conductance-based models and other physical-chemical systems. | es_ES |
dc.description.sponsorship | SR would like to acknowledge Ikerbasque (The Basque Foundation
for Science). Moreover, SR and JUA would like to thank for the fact that this research is
supported by the Basque Government through the BERC 2018-2021 program and by the
Spanish State Research Agency through BCAM Severo Ochoa excellence accreditation SEV-
2017-0718 and through project RTI2018-093860-B-C21 funded by (AEI/FEDER, UE) and
acronym “MathNEURO”. MD acknowledges BCAM’s hospitality during a visiting fellowship
in the summer 2019. | es_ES |
dc.language.iso | eng | es_ES |
dc.publisher | Springer | es_ES |
dc.relation | info:eu-repo/grantAgreement/MICIN/RTI2018-093860-B-C21 | |
dc.rights | info:eu-repo/semantics/openAccess | es_ES |
dc.title | Inflection, Canards and Folded Singularities in Excitable Systems: Application to a 3D FitzHugh–Nagumo Model | es_ES |
dc.type | info:eu-repo/semantics/article | es_ES |
dc.rights.holder | © 2020, Springer Science Business Media, LLC, part of Springer Nature | * |
dc.relation.publisherversion | https://link.springer.com/article/10.1007/s00332-020-09650-9 | |
dc.identifier.doi | /10.1007/s00332-020-09650-9 | |
dc.departamentoes | Matemáticas | es_ES |
dc.departamentoeu | Matematika | es_ES |