  Inspecting a $p$-dimensional parameter space by means of $(p-1)$-dimensional
slices, changes can be detected that are only determined by the geometry of the
manifolds that compose the bifurcation set. We refer to these changes as
geometric bifurcations. They can be understood within the framework of the
theory of singularities for differentiable mappings and, particularly, the
Morse Theory. Working with a three-dimensional parameter space, geometric
bifurcations are discussed in the context of two models of neuron activity: the
Hindmarsh-Rose and the FitzHugh-Nagumo systems. Both are fast-slow systems with
a small parameter that controls the time scale of a slow variable. Geometric
bifurcations are observed on slices corresponding to fixed values of this
distinguished small parameter.
