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A model of a biological neuron is a mathematical description of the properties of nerve cells, or neurons, that is designed to accurately describe and predict its biological processes. One of the most successful neuron models is the Hodgkin–Huxley model, for which Hodgkin and Huxley won the 1963 Nobel Prize in physiology or medicine.
In the following generalized system of equations for parabolic bursting, the values of describe the membrane potential and ion channels, typical of many conductance-based biological neuron models. Slow oscillations are controlled by , and ultimately described by . These slow oscillations can be, for example, slow fluctuations in calcium ...
Biological neuron models, also known as spiking neuron models, [1] are mathematical descriptions of the conduction of electrical signals in neurons. Neurons (or nerve cells) are electrically excitable cells within the nervous system , able to fire electric signals, called action potentials , across a neural network.
Oscillations are an important type of cell signaling characterized by the periodic change of the system in time. [1] Oscillations can take place in a biological system in a multitude of ways. Positive feedback loops, on their own or in combination with negative feedback are a common feature of oscillating biological systems. [2]
It was named after Richard FitzHugh (1922–2007) [2] who suggested the system in 1961 [3] and Jinichi Nagumo et al. who created the equivalent circuit the following year. [4]In the original papers of FitzHugh, this model was called Bonhoeffer–Van der Pol oscillator (named after Karl-Friedrich Bonhoeffer and Balthasar van der Pol) because it contains the Van der Pol oscillator as a special ...
For example, a first neuron inhibits a second one while it fires, however, it also induces slow depolarization in the second neuron. This is followed by the release of an action potential from the second neuron as a result of depolarization, which acts on the first in a similar fashion. This allows for self-sustaining patterns of oscillation.
The periods of these oscillations can vary depending on the biological system, with examples such as: (1) neural responses can change within a millisecond to quickly relay information; (2) In cardiac and respiratory changes that occur throughout the day, could be within seconds; (3) circadian rhythms may vary throughout a series of days; (4 ...
Neuronal activity at the microscopic level has a stochastic character, with atomic collisions and agitation, that may be termed "noise." [4] While it isn't clear on what theoretical basis neuronal responses involved in perceptual processes can be segregated into a "neuronal noise" versus a "signal" component, and how such a proposed dichotomy could be corroborated empirically, a number of ...