  We propose a generalization of the neurotransmitter release model proposed in
\emph{Rodrigues et al. (PNAS, 2016)}. We increase the complexity of the
underlying slow-fast system by considering a degree-four polynomial as
parametrization of the critical manifold. We focus on the possible transient
and asymptotic dynamics, exploiting the so-called entry-exit function to
describe slow parts of the dynamics. We provide extensive numerical
simulations, complemented by numerical bifurcation analysis.
