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The distinct qualitative behavior exhibited by neuron at externally applied current stimuli is well known in the Hodgkin-Huxley model (HH model). The resting state and periodic firings in neuron correspond to solutions of the HH model having stable fixed points and unstable fixed point (periodic solutions through Hopf bifurcation points). The one-parameter bifurcation with respect to externally applied current stimuli suggests a periodic window between two stable fixed point solutions in the HH model. The externally applied sinusoidal current stimuli generate periodic firings at very low current and a large periodic region is observed. The generations of limit cycles and possible chaotic behavior in the HH model is explored through numerical simulations extensively.

Periodic firings in neurons with external sinusoidal applied current