  Small dorsal root ganglion (DRG) neurons are primary nociceptors which are
responsible for sensing pain. Elucidation of their dynamics is essential for
understanding and controlling pain. To this end, we present a numerical
bifurcation analysis of a small DRG neuron model in this paper. The model is of
Hodgkin-Huxley type and has 9 state variables. It consists of a
Na$\mathrm{_v}$1.7 and a Na$\mathrm{_v}$1.8 sodium channel, a leak channel, a
delayed rectifier potassium and an A-type transient potassium channel. The
dynamics of this model strongly depends on the maximal conductances of the
voltage-gated ion channels and the external current, which can be adjusted
experimentally. We show that the neuron dynamics are most sensitive to the
Na$\mathrm{_v}$1.8 channel maximal conductance ($\bar{g}_{1.8}$). Numerical
bifurcation analysis shows that depending on $\bar{g}_{1.8}$ and the external
current, different parameter regions can be identified with stable steady
states, periodic firing of action potentials, mixed-mode oscillations (MMOs),
and bistability between stable steady states and stable periodic firing of
action potentials. We illustrate and discuss the transitions between these
different regimes. We further analyze the behavior of MMOs. Within this region,
bifurcation analysis shows a sequence of isolated periodic solution branches
with one large action potential and a number of small amplitude peaks per
period. A closer inspection reveals more complex concatenated MMOs in between
these periodic MMOs branches, forming Farey sequences. Lastly, we also find
small solution windows with aperiodic oscillations, which seem to be chaotic.
The dynamical patterns found here as a function of different parameters contain
information of translational importance as their relation to pain sensation and
its intensity is a potential source of insight into controlling pain.
