Computer algebra systems present a natural environment for studying dynamical
mathematical models depending on parameters. The main goal of such kind of studies is to
reduce and simplify the initial system to its topological normal form.
This requires different transformations, involving  steady states
computation, evaluation of genericity conditions etc.
In many cases however especially in more complicated models,
it is not possible to fulfill all manipulations symbolically.
This necessarily leads to applying self-validating numerical methods at some
steps of the needed transformations.

We demonstrate the above approaches in studying
one-parameter local bifurcations of bioprocess dynamical models.