000135508 001__ 135508 000135508 005__ 20260112133349.0 000135508 0247_ $$2doi$$a10.1038/s41598-024-61574-6 000135508 0248_ $$2sideral$$a138643 000135508 037__ $$aART-2024-138643 000135508 041__ $$aeng 000135508 100__ $$0(orcid)0000-0002-8089-343X$$aBarrio, Roberto$$uUniversidad de Zaragoza 000135508 245__ $$aExploring the geometry of the bifurcation sets in parameter space 000135508 260__ $$c2024 000135508 5060_ $$aAccess copy available to the general public$$fUnrestricted 000135508 5203_ $$aBy studying a nonlinear model by inspecting a p-dimensional parameter space through (P-1)dimensional cuts, one can detect changes that are only determined by the geometry of the manifolds that make up the bifurcation set. We refer to these changes as geometric bifurcations. They can be understood within the framework of the theory of singularities for differentiable mappings and, in particular, of the Morse Theory. Working with a three-dimensional parameter space, geometric bifurcations are illustrated in two models of neuron activity: the Hindmarsh–Rose and the FitzHugh–Nagumo systems. Both are fast-slow systems with a small parameter that controls the time scale of a slow variable. Geometric bifurcations are observed on slices corresponding to fixed values of this distinguished small parameter, but they should be of interest to anyone studying bifurcation diagrams in the context of nonlinear phenomena. 000135508 536__ $$9info:eu-repo/grantAgreement/ES/AEI/PID2021-122961NB-I00$$9info:eu-repo/grantAgreement/ES/DGA/E24-23R 000135508 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttps://creativecommons.org/licenses/by/4.0/deed.es 000135508 590__ $$a3.9$$b2024 000135508 592__ $$a0.874$$b2024 000135508 591__ $$aMULTIDISCIPLINARY SCIENCES$$b25 / 135 = 0.185$$c2024$$dQ1$$eT1 000135508 593__ $$aMultidisciplinary$$c2024$$dQ1 000135508 594__ $$a6.7$$b2024 000135508 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000135508 700__ $$aIbáñez, Santiago 000135508 700__ $$aPérez, Lucía 000135508 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000135508 773__ $$g14, 1 (2024), 10900 [14 pp.]$$pSci. rep. (Nat. Publ. Group)$$tScientific reports (Nature Publishing Group)$$x2045-2322 000135508 8564_ $$s4132998$$uhttps://zaguan.unizar.es/record/135508/files/texto_completo.pdf$$yVersión publicada 000135508 8564_ $$s2013467$$uhttps://zaguan.unizar.es/record/135508/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000135508 909CO $$ooai:zaguan.unizar.es:135508$$particulos$$pdriver 000135508 951__ $$a2026-01-12-13:18:27 000135508 980__ $$aARTICLE