  Evidence from experimental studies shows that oscillations due to
electro-mechanical coupling can be generated spontaneously in smooth muscle
cells. Such cellular dynamics are known as \textit{pacemaker dynamics}. In this
article we address pacemaker dynamics associated with the interaction of
$\text{Ca}^{2+}$ and $\text{K}^+$ fluxes in the cell membrane of a smooth
muscle cell. First we reduce a pacemaker model to a two-dimensional system
equivalent to the reduced Morris-Lecar model and then perform a detailed
numerical bifurcation analysis of the reduced model. Existing bifurcation
analyses of the Morris-Lecar model concentrate on external applied current
whereas we focus on parameters that model the response of the cell to changes
in transmural pressure. We reveal a transition between Type I and Type II
excitabilities with no external current required. We also compute a
two-parameter bifurcation diagram and show how the transition is explained by
the bifurcation structure.
