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. 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 stimulatio