Resumen de Dynamics of excitable cells: spike-adding phenomena in action

Roberto Barrio Gil , Santiago Francisco Ibáñez Mesa , Jorge Alberto Jover Galtier, Álvaro Lozano Robledo, M. Angeles Martínez, Ana Mayora Cebollero, Carmen Mayora Cebollero, Lucía Pérez Pérez, Sergio Serrano Pastor , Rubén Vigara

• We 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.