Strange nonchaotic oscillations in the quasiperiodically forced Hodgkin–Huxley neuron

Abstract

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, a new type of strange nonchaotic (SN) oscillating states (that are geometrically strange but have no positive Lyapunov exponents) is 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.