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Modeling a Spiking Neuron II - Firing Rate Model

The firing rate model is used in most artificial neural networks. The dynamics of this model is exactly the same as the integrate-and-fire model discussed above. The only difference here is that the firing rate f is assumed to be a continuous and nonlinear function of V(t)

f=g(V)

As function g relates membrane potential (voltage in Volt) to firing rate (frequency in Hertz), it has the dimension of Hertz/Volt. But we could just treat g as a dimensionless function for simplicity if we can accept to treat f as if it is a voltage representing the signal intensity transmitted along the axon (not to be confused with the intensity of the action potentials).

The most commonly used g is a sigmoidal function of V(t)

\begin{displaymath}f=\frac{1}{1+e^{-c*V}} \end{displaymath}

where c is some constant. The continuous firing rate model is obtained by replacing the switch and the spike generator with a block simulating function g, as shown in the figure.

../figures/continuousfiringmodel.gif

The sigmoidal function is used in many neural network models. Note that the constant c determines the slope of the transition.

../figures/sigmoidal.gif

Several points need to be made regarding this firing rate model:


next up previous
Next: Neural networks Up: No Title Previous: Adapting Model
Ruye Wang
1999-09-20