Lecture

Neuron Models: Type I and Type II

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

This lecture covers the reduction of detail in two-dimensional neuron models, focusing on Type I and Type II models. It discusses the firing threshold, separation of time scales, and the nonlinear integrate-and-fire model. The lecture also explores the Hopf bifurcation and the stability of fixed points.

In MOOC

Neuronal Dynamics - Computational Neuroscience of Single Neurons

This course gives an introduction to the field of theoretical and computational neuroscience with a focus on models of single neurons. Neurons encode information about stimuli in a sequence of short electrical pulses (spikes).

Official source

Related concepts (30)

Biological neuron model

Biological neuron models, also known as a spiking neuron models, are mathematical descriptions of the properties of certain cells in the nervous system that generate sharp electrical potentials across their cell membrane, roughly one millisecond in duration, called action potentials or spikes (Fig. 2). Since spikes are transmitted along the axon and synapses from the sending neuron to many other neurons, spiking neurons are considered to be a major information processing unit of the nervous system.

Computational neuroscience

Computational neuroscience (also known as theoretical neuroscience or mathematical neuroscience) is a branch of neuroscience which employs mathematical models, computer simulations, theoretical analysis and abstractions of the brain to understand the principles that govern the development, structure, physiology and cognitive abilities of the nervous system. Computational neuroscience employs computational simulations to validate and solve mathematical models, and so can be seen as a sub-field of theoretical neuroscience; however, the two fields are often synonymous.

Fixed point (mathematics)

hatnote|1=Fixed points in mathematics are not to be confused with other uses of "fixed point", or stationary points where math|1=f(x) = 0. In mathematics, a fixed point (sometimes shortened to fixpoint), also known as an invariant point, is a value that does not change under a given transformation. Specifically for functions, a fixed point is an element that is mapped to itself by the function. Formally, c is a fixed point of a function f if c belongs to both the domain and the codomain of f, and f(c) = c.

Fixed-point iteration

In numerical analysis, fixed-point iteration is a method of computing fixed points of a function. More specifically, given a function defined on the real numbers with real values and given a point in the domain of , the fixed-point iteration is which gives rise to the sequence of iterated function applications which is hoped to converge to a point . If is continuous, then one can prove that the obtained is a fixed point of , i.e., More generally, the function can be defined on any metric space with values in that same space.

Fixed-point theorem

In mathematics, a fixed-point theorem is a result saying that a function F will have at least one fixed point (a point x for which F(x) = x), under some conditions on F that can be stated in general terms. The Banach fixed-point theorem (1922) gives a general criterion guaranteeing that, if it is satisfied, the procedure of iterating a function yields a fixed point.

Related lectures (64)

Analysis of a 2D neuron model: Constant input MOOC: Neuronal Dynamics - Computational Neuroscience of Single Neurons

Explores the behavior of a 2D neuron model with constant input.

In Silico Neuroscience: Ion Channels and Neuronal Models

Explores detailed modeling of ion channels and neuronal morphologies in in silico neuroscience, covering neuron classification, ion channel kinetics, and experimental observations.

Firing Threshold in 2D Models MOOC: Neuronal Dynamics - Computational Neuroscience of Single Neurons

Explores firing thresholds in 2D neuron models, pulse input, delayed spike initiation, and the FitzHugh-Nagumo model.

Models and data MOOC: Neuronal Dynamics - Computational Neuroscience of Single Neurons

Covers the optimization of neuron models for coding and decoding in computational neuroscience.

Scientific Computing in Neuroscience