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The theta model, or Ermentrout–Kopell canonical model, is a biological neuron model originally developed to mathematically describe neurons in the animal Aplysia. [1] The model is particularly well-suited to describe neural bursting , which is characterized by periodic transitions between rapid oscillations in the membrane potential followed ...
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.
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.
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.
Theta oscillations, typically defined within the frequency range of 4–7 Hz, play a significant role in various cognitive processes, including learning and cognitive control. Research has shown that these oscillations are closely associated with memory encoding and retrieval, emotional regulation, and the maintenance of cognitive tasks.
Phase resetting in neurons is a behavior observed in different biological oscillators and plays a role in creating neural synchronization as well as different processes within the body. Phase resetting in neurons is when the dynamical behavior of an oscillation is shifted. This occurs when a stimulus perturbs the phase within an oscillatory ...
The FitzHugh–Nagumo model (FHN) describes a prototype of an excitable system (e.g., a neuron). It is an example of a relaxation oscillator because, if the external stimulus I ext {\displaystyle I_{\text{ext}}} exceeds a certain threshold value, the system will exhibit a characteristic excursion in phase space , before the variables v ...
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.