Sigmoidal function

Question

Can someone explain what a sigmoidal function is? I have "$S(x)$ is a sigmoidal function with $S'(x)\ge0$ and $\lim_{x\rightarrow-\infty}S(x)=0$

but I really don't understand what $S(x)$ is

I found an expression for $S(x)$ using the Naka-Rushkin function and it said that $S(x)=\frac{MP^N}{\phi^N+P^N}$ for $P\ge0$ or $=0$ for $P<0$ but the didn't really help with my understanding

I don't know if this is relevant, but I am examining neurons coupled together in a network and their activity is described by this sigmoidal function

Many different functions are called "sigmoidal", depending on the application. One example is tanh(x). — user_of_math, Dec 16 '14 at 23:05
@user_of_math oh ok, so it is just a type of function, not the name of a specific equation? — user181304, Dec 16 '14 at 23:06
Yes. Take a look at http://en.wikipedia.org/wiki/Sigmoid_function — user_of_math, Dec 16 '14 at 23:07

score 0 · Accepted Answer · edited Apr 13 '17 at 12:44

A sigmoid is -roughly speaking- an increasing differentiable function with horizontal asymptotes at arbitrarily small /big real values. It assumes a characteristic "S" shape. There exist many different examples of sigmoidal functions, whose applications are numerous. Please, have a look at this link for more details.

An important example of sigmoid is given by the logistic function which is widely used in machine learning and statistics. A comparison of logistic and probit functions and subsequent modelling can be found here.

Sigmoidal function

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