Lecture

Reduction to 2 dimensions: Exploiting similarities

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 the Hodgkin-Huxley model to 2 dimensions by exploiting similarities and correlations between variables. It discusses the separation of time scales, the role of nullclines, stability of fixed points, and the analysis of 2D neuron models. The dynamics of h and n are shown to be similar, leading to the nonlinear integrate-and-fire model.

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 (21)

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.

Neuron

Within a nervous system, a neuron, neurone, or nerve cell is an electrically excitable cell that fires electric signals called action potentials across a neural network. Neurons communicate with other cells via synapses - specialized connections that commonly use minute amounts of chemical neurotransmitters to pass the electric signal from the presynaptic neuron to the target cell through the synaptic gap. The neuron is the main component of nervous tissue in all animals except sponges and placozoa.

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.

Machiavellianism (psychology)

In the field of personality psychology, Machiavellianism is a personality trait centered on manipulativeness, callousness, and indifference to morality, with a strategic focus on self interest. Psychologists Richard Christie and Florence Geis named the trait after Niccolò Machiavelli, as they used edited and truncated statements inspired by his works to study variations in human behaviors. Their Mach IV test, a 20-question, Likert-scale personality survey, became the standard self-assessment tool and scale of the Machiavellianism construct.

Neuroscience

Neuroscience is the scientific study of the nervous system (the brain, spinal cord, and peripheral nervous system), its functions and disorders. It is a multidisciplinary science that combines physiology, anatomy, molecular biology, developmental biology, cytology, psychology, physics, computer science, chemistry, medicine, statistics, and mathematical modeling to understand the fundamental and emergent properties of neurons, glia and neural circuits.

Related lectures (64)

Scientific Computing in Neuroscience

Explores the history and tools of scientific computing in neuroscience, emphasizing the simulation of neurons and networks.

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

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

Leaky Integrate-and-Fire Model MOOC: Neuronal Dynamics - Computational Neuroscience of Single Neurons

Explores the Leaky Integrate-and-Fire Model in computational neuroscience, emphasizing single neuron dynamics.

Generalized Integrate-and-Fire Models MOOC: Neuronal Dynamics - Computational Neuroscience of Single Neurons

Explores the Generalized Integrate-and-Fire Model and the Nonlinear Integrate-and-Fire Model.

Dendrite as a Cable MOOC: Neuronal Dynamics - Computational Neuroscience of Single Neurons