Dynamics of excitable cells: spike-adding phenomena in action

• Roberto Barrio ^[1] ; Santiago Ibáñez ^[2] ; Jorge A. Jover-Galtier ^[1] ; Álvaro Lozano ^[1] ; M. Ángeles Martínez ^[1] ; Ana Mayora-Cebollero ^[1] ; Carmen Mayora-Cebollero ^[1] ; Lucía Pérez ^[2] ; Sergio Serrano ^[1] ; Rubén Vigara ^[1]
  1. [1] Universidad de Zaragoza

     Universidad de Zaragoza

     Zaragoza, España

     
  2. [2] Universidad de Oviedo

     Universidad de Oviedo

     Oviedo, España

     
• Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 81, Nº. Extra 1, 2024, págs. 113-146
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.