doi:10.1007/s40324-023-00328-2engBarrio, RobertoIbáñez, SantiagoJover-Galtier, Jorge A.Lozano, ÁlvaroMartínez, M. ÁngelesMayora-Cebollero, AnaMayora-Cebollero, CarmenPérez, LucíaSerrano, SergioVigara, RubénDynamics of excitable cells: spike-adding phenomena in actionART-2024-134466We study the dynamics of action potentials of some electrically excitable cells: neurons and cardiac muscle cells. Bursting, following a fast–slow dynamics, is the most characteristic behavior of these dynamical systems, and the number of spikes may change due to spike-adding phenomenon. Using analytical and numerical methods we give, by focusing on the paradigmatic 3D Hindmarsh–Rose neuron model, a review of recent results on the global organization of the parameter space of neuron models with bursting regions occurring between saddle-node and homoclinic bifurcations (fold/hom bursting). We provide a generic overview of the different bursting regimes that appear in the parametric phase space of the model and the bifurcations among them. These techniques are applied in two realistic frameworks: insect movement gait changes and the appearance of Early Afterdepolarizations in cardiac dynamics.2024http://zaguan.unizar.es/record/12695210.1007/s40324-023-00328-2http://zaguan.unizar.es/record/126952oai:zaguan.unizar.es:126952info:eu-repo/grantAgreement/ES/AEI/PID2021-122961NB-I00info:eu-repo/grantAgreement/ES/DGA/E22-20Rinfo:eu-repo/grantAgreement/ES/DGA-FSE/E24-20Rinfo:eu-repo/grantAgreement/ES/DGA/LMP94_21info:eu-repo/grantAgreement/ES/MCIU/FPU20-04039info:eu-repo/grantAgreement/ES/MICINN/PGC2018-096026-B-I00info:eu-repo/grantAgreement/ES/MICINN-AEI/PID2020-113052GB-I00info:eu-repo/grantAgreement/ES/MINECO-FEDER/MTM2017-87697-PSEMA Journal 81 (2024), 113-146byhttps://creativecommons.org/licenses/by/4.0/deed.esinfo:eu-repo/semantics/openAccess