Phase-locking and chaos in a silent Hodgkin-Huxley neuron exposed to sinusoidal electric field

Neuronal firing patterns are related to the information processing in neural system. This paper investigates the response characteristics of a silent Hodgkin-Huxley neuron to the stimulation of externally-applied sinusoidal electric field. The neuron exhibits both p:q phase-locked (i.e. a periodic oscillation defined as p action potentials generated by q cycle stimulations) and chaotic behaviors, depending on the values of stimulus frequencies and amplitudes. In one-parameter space, a rich bifurcation structure including period-adding without chaos and phase-locking alternated with chaos suggests frequency discrimination of the neuronal firing patterns. Furthermore, by mapping out Arnold tongues, we partition the amplitude-frequency parameter space in terms of the qualitative behaviors of the neuron. Thus the neuron's information (firing patterns) encodes the stimulus information (amplitude and frequency), and vice versa.