  The phenomenon of an excitable system producing a pulse under external or
internal stimulation may be interpreted as a stochastic escape problem. This
work addresses this issue by examining the Morris-Lecar neural model driven by
symmetric \alpha-stable L\'evy motion. Two deterministic indices: the first
escape probability and the mean first exit time, are adopted to analyse the
state transition in this stochastic model. We calculate both indices in order
to understand the transition from the escape region to the target region, and
the area of higher indices in escape region. Additionally, we consider the
special case of (Gaussian) Brownian motion to compare with (non-Gaussian)
L\'evy motion case. Our main results indicate that higher first escape
probability promotes the transition, while the mean first exit time reflects
the stability of the rest state with the selected escape region. The higher
non-Gaussianity index and relatively small noise intensity are more prone to
produce spikes. Moreover, by calculating both deterministic indices as
functions of noise intensity ratio and non-Gaussianity index, we find that the
effect of ion channel noise is more pronounced on the stochastic Morris-Lecar
model than noise in the current. This work provides some mathematical
understanding about the impact of non-Gaussian, heavy-tailed, burst-like
fluctuations on excitable systems such as the Morris-Lecar system.
