  We analyze a piecewise-linear FitzHugh-Nagumo model. The system exhibits a
canard near which both small amplitude and large amplitude periodic orbits
exist. The addition of small noise induces mixed-mode oscillations (MMOs) in
the vicinity of the canard point. We determine the effect of each model
parameter on the stochastically driven MMOs. In particular we show that any
parameter variation (such as a modification of the piecewise-linear function in
the model) that leaves the ratio of noise amplitude to time-scale separation
unchanged typically has little effect on the width of the interval of the
primary bifurcation parameter over which MMOs occur. In that sense, the MMOs
are robust. Furthermore we show that the piecewise-linear model exhibits MMOs
more readily than the classical FitzHugh-Nagumo model for which a cubic
polynomial is the only nonlinearity. By studying a piecewise-linear model we
are able to explain results using analytical expressions and compare these with
numerical investigations.
