  Comparing neuronal bursting models (NBM) with slow-fast autonomous dynamical
systems (S-FADS), it appears that the specific features of a (NBM) do not allow
a determination of the analytical slow manifold equation with the singular
approximation method. So, a new approach based on Differential Geometry,
generally used for (S-FADS), is proposed. Adapted to (NBM), this new method
provides three equivalent manners of determination of the analytical slow
manifold equation. Application is made for the three-variables model of
neuronal bursting elaborated by Hindmarsh and Rose which is one of the most
used mathematical representation of the widespread phenomenon of oscillatory
burst discharges that occur in real neuronal cells.
