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The adaptive exponential integrate-and-fire model inherits the experimentally derived voltage nonlinearity [4] of the exponential integrate-and-fire model. But going beyond this model, it can also account for a variety of neuronal firing patterns in response to constant stimulation, including adaptation, bursting and initial bursting.
The theta model, or Ermentrout–Kopell canonical Type I model, is mathematically equivalent to the quadratic integrate-and-fire model which in turn is an approximation to the exponential integrate-and-fire model and the Hodgkin-Huxley model. It is called a canonical model because it is one of the generic models for constant input close to the ...
Toyesh Prakash Sharma, Etisha Sharma, "Putting Forward Another Generalization Of The Class Of Exponential Integrals And Their Applications.," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.10, Issue.2, pp.1-8, 2023.
The biologically inspired Hodgkin–Huxley model of a spiking neuron was proposed in 1952. This model describes how action potentials are initiated and propagated. . Communication between neurons, which requires the exchange of chemical neurotransmitters in the synaptic gap, is described in various models, such as the integrate-and-fire model, FitzHugh–Nagumo model (1961–1962), and ...
One of his main contributions was to propose the integrate-and-fire model of the neuron in a seminal article published in 1907. [2] Today, this model of the neuron is still one of the most popular models in computational neuroscience for both cellular and neural networks studies, as well as in mathematical neuroscience because of its simplicity.
NEST aims at high accuracy and precision of its simulations [2] Each neuron model has its appropriate solver and many models have unit tests. If possible, exact integration [3] is used. By default, spikes fall onto the grid, defined by the simulation time-step. Some models support spike-exchange in continuous time. [4]
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 ...
The authors used a network of theta models in favor of a network of leaky integrate-and-fire (LIF) models due to two primary advantages: first, the theta model is continuous, and second, the theta model retains information about "the delay between the crossing of the spiking threshold and the actual firing of an action potential".