  Many research works deal with chaotic neural networks for various fields of
application. Unfortunately, up to now these networks are usually claimed to be
chaotic without any mathematical proof. The purpose of this paper is to
establish, based on a rigorous theoretical framework, an equivalence between
chaotic iterations according to Devaney and a particular class of neural
networks. On the one hand we show how to build such a network, on the other
hand we provide a method to check if a neural network is a chaotic one.
Finally, the ability of classical feedforward multilayer perceptrons to learn
sets of data obtained from a dynamical system is regarded. Various Boolean
functions are iterated on finite states. Iterations of some of them are proven
to be chaotic as it is defined by Devaney. In that context, important
differences occur in the training process, establishing with various neural
networks that chaotic behaviors are far more difficult to learn.
