Classification of fold/hom and fold/Hopf spike-adding phenomena
| Autor: | Roberto Barrio, Lucía Relea Pérez, Santiago Ibáñez, Sergio Serrano |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Physics
Sequence Pure mathematics Quantitative Biology::Neurons and Cognition Fold (higher-order function) Applied Mathematics Chaotic General Physics and Astronomy Statistical and Nonlinear Physics 01 natural sciences 010305 fluids & plasmas Bursting 0103 physical sciences Periodic orbits Spike (software development) 010306 general physics Crucial point Mathematical Physics |
| Zdroj: | RUO. Repositorio Institucional de la Universidad de Oviedo instname RUO: Repositorio Institucional de la Universidad de Oviedo Universidad de Oviedo (UNIOVI) |
| ISSN: | 1089-7682 |
| Popis: | The Hindmarsh–Rose neural model is widely accepted as an important prototype for fold/hom and fold/Hopf burstings. In this paper, we are interested in the mechanisms for the production of extra spikes in a burst, and we show the whole parametric panorama in an unified way. In the fold/hom case, two types are distinguished: a continuous one, where the bursting periodic orbit goes through bifurcations but persists along the whole process and a discontinuous one, where the transition is abrupt and happens after a sequence of chaotic events. In the former case, we speak about canard-induced spike-adding and in the second one, about chaos-induced spike-adding. For fold/Hopf bursting, a single (and continuous) mechanism is distinguished. Separately, all these mechanisms are presented, to some extent, in the literature. However, our full perspective allows us to construct a spike-adding map and, more significantly, to understand the dynamics exhibited when borders are crossed, that is, transitions between types of processes, a crucial point not previously studied. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|