Classification of fold/hom and fold/Hopf spike-adding phenomena

Barrio R. (Universidad de Zaragoza) ; Ibáñez S. ; Pérez L. ; Serrano S. (Universidad de Zaragoza)

Resumen: The Hindmarsh-Rose neural model is widely accepted as an important prototype for fold/hom and fold/Hopf burstings. In this paper, we are interested in the mechanisms for the production of extra spikes in a burst, and we show the whole parametric panorama in an unified way. In the fold/hom case, two types are distinguished: a continuous one, where the bursting periodic orbit goes through bifurcations but persists along the whole process and a discontinuous one, where the transition is abrupt and happens after a sequence of chaotic events. In the former case, we speak about canard-induced spike-adding and in the second one, about chaos-induced spike-adding. For fold/Hopf bursting, a single (and continuous) mechanism is distinguished. Separately, all these mechanisms are presented, to some extent, in the literature. However, our full perspective allows us to construct a spike-adding map and, more significantly, to understand the dynamics exhibited when borders are crossed, that is, transitions between types of processes, a crucial point not previously studied. © 2021 Author(s).

Idioma: Inglés

DOI: 10.1063/5.0037942

Año: 2021

Publicado en: CHAOS 31, 4 (2021), 043120 [15 pp]
ISSN: 1054-1500

Factor impacto JCR: 3.741 (2021)

Categ. JCR: PHYSICS, MATHEMATICAL rank: 7 / 56 = 0.125 (2021) - Q1 - T1
Categ. JCR: MATHEMATICS, APPLIED rank: 17 / 267 = 0.064 (2021) - Q1 - T1

Factor impacto CITESCORE: 5.8 - Mathematics (Q1) - Physics and Astronomy (Q1)

Factor impacto SCIMAGO: 1.009 - Applied Mathematics (Q1) - Statistical and Nonlinear Physics (Q1) - Physics and Astronomy (miscellaneous) (Q1) - Mathematical Physics (Q1)

Financiación: info:eu-repo/grantAgreement/ES/DGA-FSE/E24-17R
Financiación: info:eu-repo/grantAgreement/ES/DGA-FSE/LMP124-18
Financiación: info:eu-repo/grantAgreement/ES/MICINN/PGC2018-096026-B-I00
Financiación: info:eu-repo/grantAgreement/ES/MICINN-FEDER/PID2019-105674RB-I00
Financiación: info:eu-repo/grantAgreement/ES/MINECO-FEDER/MTM2017-87697-P

Tipo y forma: Artículo (PostPrint)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)