000129863 001__ 129863 000129863 005__ 20240112163659.0 000129863 0247_ $$2doi$$a10.1063/5.0037942 000129863 0248_ $$2sideral$$a126916 000129863 037__ $$aART-2021-126916 000129863 041__ $$aeng 000129863 100__ $$0(orcid)0000-0002-8089-343X$$aBarrio R.$$uUniversidad de Zaragoza 000129863 245__ $$aClassification of fold/hom and fold/Hopf spike-adding phenomena 000129863 260__ $$c2021 000129863 5060_ $$aAccess copy available to the general public$$fUnrestricted 000129863 5203_ $$aThe 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). 000129863 536__ $$9info:eu-repo/grantAgreement/ES/DGA-FSE/E24-17R$$9info:eu-repo/grantAgreement/ES/DGA-FSE/LMP124-18$$9info:eu-repo/grantAgreement/ES/MICINN/PGC2018-096026-B-I00$$9info:eu-repo/grantAgreement/ES/MICINN-FEDER/PID2019-105674RB-I00$$9info:eu-repo/grantAgreement/ES/MINECO-FEDER/MTM2017-87697-P 000129863 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000129863 590__ $$a3.741$$b2021 000129863 591__ $$aPHYSICS, MATHEMATICAL$$b7 / 56 = 0.125$$c2021$$dQ1$$eT1 000129863 591__ $$aMATHEMATICS, APPLIED$$b17 / 267 = 0.064$$c2021$$dQ1$$eT1 000129863 592__ $$a1.009$$b2021 000129863 593__ $$aApplied Mathematics$$c2021$$dQ1 000129863 593__ $$aStatistical and Nonlinear Physics$$c2021$$dQ1 000129863 593__ $$aPhysics and Astronomy (miscellaneous)$$c2021$$dQ1 000129863 593__ $$aMathematical Physics$$c2021$$dQ1 000129863 594__ $$a5.8$$b2021 000129863 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000129863 700__ $$aIbáñez S. 000129863 700__ $$aPérez L. 000129863 700__ $$0(orcid)0000-0002-5701-1670$$aSerrano S.$$uUniversidad de Zaragoza 000129863 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000129863 773__ $$g31, 4 (2021), 043120 [15 pp]$$pChaos$$tCHAOS$$x1054-1500 000129863 8564_ $$s7727318$$uhttps://zaguan.unizar.es/record/129863/files/texto_completo.pdf$$yPostprint 000129863 8564_ $$s3510719$$uhttps://zaguan.unizar.es/record/129863/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000129863 909CO $$ooai:zaguan.unizar.es:129863$$particulos$$pdriver 000129863 951__ $$a2024-01-12-14:09:15 000129863 980__ $$aARTICLE