  The dynamics of a model, originally proposed for a type of instability in
plastic flow, has been investigated in detail. The bifurcation portrait of the
system in two physically relevant parameters exhibits a rich variety of
dynamical behaviour, including period bubbling and period adding or Farey
sequences. The complex bifurcation sequences, characterized by Mixed Mode
Oscillations, exhibit partial features of Shilnikov and Gavrilov-Shilnikov
scenario. Utilizing the fact that the model has disparate time scales of
dynamics, we explain the origin of the relaxation oscillations using the
geometrical structure of the bent-slow manifold. Based on a local analysis, we
calculate the maximum number of small amplitude oscillations, $s$, in the
periodic orbit of $L^s$ type, for a given value of the control parameter. This
further leads to a scaling relation for the small amplitude oscillations. The
incomplete approach to homoclinicity is shown to be a result of the finite rate
of `softening' of the eigen values of the saddle focus fixed point. The latter
is a consequence of the physically relevant constraint of the system which
translates into the occurrence of back-to-back Hopf bifurcation.
