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Additionally, the motor unit action potential is an all-or-none phenomenon - once the recruitment threshold (the stimulus intensity at which a motor unit begins to fire) is reached, it fires fully. Electrical stimulation of nerves reverses the recruitment order, due to the lower resistance of the larger motor neuron axons.
To better understand how the cable equation is derived, first simplify the theoretical neuron even further and pretend it has a perfectly sealed membrane (r m =∞) with no loss of current to the outside, and no capacitance (c m = 0). A current injected into the fiber [c] at position x = 0 would move along the inside of the fiber unchanged.
The activating function represents the rate of membrane potential change if the neuron is in resting state before the stimulation. Its physical dimensions are V/s or mV/ms. In other words, it represents the slope of the membrane voltage at the beginning of the stimulation. [8]
Figure FHN: To mimick the action potential, the FitzHugh–Nagumo model and its relatives use a function g(V) with negative differential resistance (a negative slope on the I vs. V plot). For comparison, a normal resistor would have a positive slope, by Ohm's law I = GV, where the conductance G is the inverse of resistance G=1/R.
As with most neuronal models, increasing the injected current will increase the firing rate of the neuron. One consequence of the Hopf bifurcation is that there is a minimum firing rate. This means that either the neuron is not firing at all (corresponding to zero frequency), or firing at the minimum firing rate.
The activation function of a neuron is chosen to have a number of properties which either enhance or simplify the network containing the neuron. Crucially, for instance, any multilayer perceptron using a linear activation function has an equivalent single-layer network; a non -linear function is therefore necessary to gain the advantages of a ...
Mathematically, a neuron's network function () is defined as a composition of other functions (), that can further be decomposed into other functions. This can be conveniently represented as a network structure, with arrows depicting the dependencies between functions.
(ii) Even though it is a nonlinear model, it is simple enough to calculate the firing rate for constant input, and the linear response to fluctuations, even in the presence of input noise. [ 6 ] A didactive review of the exponential integrate-and-fire model (including fit to experimental data and relation to the Hodgkin-Huxley model) can be ...