Non-smooth dynamics in integrate-and-fire neuron models with dynamic threshold
The aim of this work is to introduce and study simple neuron models with a dynamic threshold: The integrate and fire with dynamic threshold and a resonate and fire with dynamic threshold. The last model is a new model raised from an initial study of the integrate and fire with a dynamic threshold. T...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2099.1/20531 |
| Acceso en línea: | https://hdl.handle.net/2099.1/20531 |
| Access Level: | acceso abierto |
| Palabra clave: | Differentiable dynamical systems Computational Neuroscience Non-Smooth, Dynamical System Integrate and Fire Resonate and Fire Dynamic Threshold Sistemes dinàmics diferenciables Teoria ergòdica Classificació AMS::37 Dynamical systems and ergodic theory::37N Applications Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics |
| Sumario: | The aim of this work is to introduce and study simple neuron models with a dynamic threshold: The integrate and fire with dynamic threshold and a resonate and fire with dynamic threshold. The last model is a new model raised from an initial study of the integrate and fire with a dynamic threshold. The characteristics of the new model are studied from a mathematical point of view specially concerning the dynamical systems theory of the non-smooth systems. . In this project we will study analytically and computationally integrate-and-fire models with dynamic threshold, reproducing behaviors observed in the real nervoussystems, using techniques from non-smooth systems. Our goal is to describe the types of spiking patterns that can generate in response to steady and periodic current stimulation |
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