  We explored the mathematical foundations of Recurrent Neural Networks
($\mathtt{RNN}$s) and three fundamental procedures: temporal rescaling,
discretisation and linearisation. These techniques provide essential tools for
characterizing $\mathtt{RNN}$s behaviour, enabling insights into temporal
dynamics, practical computational implementation, and linear approximations for
analysis. We discuss the flexible order of application of these procedures,
emphasizing their significance in modelling and analyzing $\mathtt{RNN}$s for
neuroscience and machine learning applications. We explicitly describe here
under what conditions these procedures can be interchangeable.
