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The firing neuron described above is called a spiking neuron. We will model the electrical circuit of the neuron in Section 3.6. There are two types of spiking neurons. If the stimulus remains above the threshold level and the output is a spike train, it is called the Integrate-and-Fire (IF) neuron model.
Brian is aimed at researchers developing models based on networks of spiking neurons. The general design is aimed at maximising flexibility, simplicity and users' development time. [2] Users specify neuron models by giving their differential equations in standard mathematical form as strings, create groups of neurons and connect them via ...
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 ...
The spiking neuron model by Nossenson & Messer [72] [73] [74] produces the probability of the neuron firing a spike as a function of either an external or pharmacological stimulus. [72] [73] [74] The model consists of a cascade of a receptor layer model and a spiking neuron model, as shown in Fig 4. The connection between the external stimulus ...
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 spike response model (SRM) [1] is a spiking neuron model in which spikes are generated by either a deterministic [2] or a stochastic [1] threshold process. In the SRM, the membrane voltage V is described as a linear sum of the postsynaptic potentials (PSPs) caused by spike arrivals to which the effects of refractoriness and adaptation are added.
Exponential integrate-and-fire models are widely used in the field of computational neuroscience and spiking neural networks because of (i) a solid grounding of the neuron model in the field of experimental neuroscience, (ii) computational efficiency in simulations and hardware implementations, and (iii) mathematical transparency.
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 ...