Strange Nonchaotic Oscillations in The Quasiperiodically Forced Hodgkin-Huxley Neuron

TL;DR

This study explores how quasiperiodic forcing induces strange nonchaotic oscillations in the Hodgkin-Huxley neuron, revealing new intermediate states with complex, fractal geometries distinct from classical periodic and chaotic responses.

Contribution

It demonstrates the existence of strange nonchaotic oscillations in the Hodgkin-Huxley neuron under quasiperiodic forcing, a novel finding compared to previous periodic forcing studies.

Findings

Discovery of strange nonchaotic oscillations between regular and chaotic states.

Identification of various routes to SN oscillations similar to quasiperiodically forced logistic map.

Potential observation of SN spikings in experimental squid giant axon studies.

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, 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.