  We numerically study dynamical behaviors of the quasiperiodically forced
Hodgkin-Huxley neuron and compare the dynamical responses with those for the
case of periodic stimulus. In the periodically forced case, a transition from a
periodic to a chaotic oscillation was found to occur via period doublings in
previous numerical and experimental works. We investigate the effect of the
quasiperiodic forcing on this period-doubling route to chaotic oscillation. In
contrast to the case of periodic forcing, new type of strange nonchaotic (SN)
oscillating states (that are geometrically strange but have no positive
Lyapunov exponents) are found to exist between the regular and chaotic
oscillating states as intermediate ones. Their strange fractal geometry leads
to aperiodic "complex" spikings. Various dynamical routes to SN oscillations
are identified, as in the quasiperiodically forced logistic map. These SN
spikings are expected to be observed in experiments of the quasiperiodically
forced squid giant axon.
