Bifurcation of periodic solutions of Hodgkin-Huxley model for the squid giant axon

The Hodgkin-Huxley model of the space-clamped squid giant axon is shown to admit unstable periodic solutions for current stimuli less than the stimulus at which the rest state becomes linearly unstable. The periodic solutions are demonstrated both by bifurcation theory and by numerical integration. The presence of subcritical unstable oscillations explains the discontinuous behaviour of the amplitude of the repetitive response as a function of current stimulus