  Phenomena in chemistry, biology and neuroscience are often modelled using
ordinary differential equations (ODEs) in which the right-hand-side is
comprised of terms which correspond to individual 'processes' or 'fluxes'.
Frequently, these ODEs are characterised by multiple time-scale phenomena due
to order of magnitude differences between contributing processes and the
presence of switching, i.e., dominance or sub-dominance of particular terms as
a function of state variables. We outline a heuristic procedure for the
identification of small parameters in ODE models of this kind, with a
particular emphasis on the identification of small parameters relating to
switching behaviours. This procedure is outlined informally in generality, and
applied in detail to a model for intracellular calcium dynamics characterised
by switching and multiple (more than two) time-scale dynamics. A total of five
small parameters are identified, and related to a single perturbation parameter
by a polynomial scaling law based on order of magnitude comparisons. The
resulting singular perturbation problem has a time-scale separation which
depends on the region of state space. We prove the existence and uniqueness of
stable relaxation oscillations with three distinct time-scales using a
coordinate-independent formulation of GSPT in combination with the blow-up
method. We also provide an estimate for the period of the oscillations, and
consider a number of possibilities for their onset under parameter variation.
