Dynamics of excitable cells: spike-adding phenomena in action

  1. Roberto Barrio 1
  2. Santiago Ibáñez 2
  3. Jorge A. Jover-Galtier 1
  4. Álvaro Lozano 3
  5. M. Ángeles Martínez 1
  6. Ana Mayora-Cebollero 1
  7. Carmen Mayora-Cebollero 1
  8. Lucía Pérez 2
  9. Sergio Serrano 1
  10. Rubén Vigara 1
  1. 1 Departamento de Matemática Aplicada and IUMA, Computational Dynamics Group, Universidad de Zaragoza, Spain
  2. 2 Departamento de Matemáticas, Universidad de Oviedo, Spain
  3. 3 Departamento de Matemáticas and IUMA, Computational Dynamics Group, Universidad de Zaragoza, Spain
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Journal:
SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada

ISSN: 2281-7875

Year of publication: 2024

Volume: 81

Issue: 1

Pages: 113-146

Type: Article

DOI: 10.1007/S40324-023-00328-2 DIALNET GOOGLE SCHOLAR

More publications in: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada

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Abstract

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.

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