  The three-dimensional (3D) Fitzhugh-Nagumo neuron model with inertia was
shown to exhibit a chaotic mixed-mode dynamics composed of large-amplitude
spikes separated by an irregular number of small-amplitude chaotic
oscillations. In contrast to the standard 2D Fitzhugh-Nagumo model driven by
noise, the interspike-intervals distribution displays a complex arrangement of
sharp peaks related to the unstable periodic orbits of the chaotic attractor.
For many ranges of parameters controlling the excitability of the system, we
observe that chaotic mixed-mode states consist of lapses of nearly regular
spiking interleaved by others of highly irregular one. We explore here the
emergence of these structures and show their correspondence to the intermittent
transitions to chaos. In fact, the average residence time in the
nearly-periodic firing state, obeys the same scaling law -- as a function of
the control parameter -- than the one at the onset type I intermittency for
dynamical systems in the vicinity of a saddle node bifurcation. We hypothesize
that this scenario is also present in a variety of slow-fast neuron models
characterized by the coexistence of a two-dimensional fast manifold and a
one-dimensional slow one.
