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
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.